Self-adjoint Operators with Inner Singularities and Pontryagin Spaces View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2000

AUTHORS

Aad Dijksma , Heinz Langer , Yuri Shondin , Chris Zeinstra

ABSTRACT

Let A0 be an unbounded self-adjoint operator in a Hilbert space H0 and let χ be a generalized element of order — m — 1 in the rigging associated with A0 and the inner product 〈·, ·〉0 of H0. In [S1, S2, S3] operators Ht, t · R ∪ ∞, are defined which serve as an interpretation for the family of operators A0 + t-1 〈·, χ〉0 χ. The second summand here contains the inner singularity mentioned in the title. The operators Ht act in Pontryagin spaces of the form πm = H0⊕Cm⊕Cmwhere the direct summand space Cm ⊕ Cmis provided with an indefinite inner product. They can be interpreted both as a canonical extension of some symmetric operator S in πm and also as extensions of a one-dimensional restriction S0 of A0 in H0 and hence they can be characterized by a class of Straus extensions of S0 as well as via M.G. Krein’s formulas for (generalized) resolvents. In this paper we describe both these realizations explicitly and study their spectral properties. A main role is played by a special class of Q-functions. Factorizations of these functions correspond to the separation of the nonpositive type spectrum from the positive spectrum of Ht. As a consequence, in Subsection 7.3 a family of self-adjoint Hilbert space operators is obtained which can serve as a nontrivial quantum model associated with the operators A0 + t-1 〈·, χ〉0 χ. More... »

PAGES

105-175

Book

TITLE

Operator Theory and Related Topics

ISBN

978-3-0348-9557-6
978-3-0348-8413-6

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-8413-6_8

DOI

http://dx.doi.org/10.1007/978-3-0348-8413-6_8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1000870627


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Groningen", 
          "id": "https://www.grid.ac/institutes/grid.4830.f", 
          "name": [
            "Department of Mathematics, University of Groningen, P.O. Box 800, 9700, AV Groningen, The Netherlands"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Dijksma", 
        "givenName": "Aad", 
        "id": "sg:person.013762723211.39", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013762723211.39"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "TU Wien", 
          "id": "https://www.grid.ac/institutes/grid.5329.d", 
          "name": [
            "Department of Mathematics, Technical University of Vienna, Wiedner Haupsstrasse 8-10/1411, A-1040, Vienna, Austria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Langer", 
        "givenName": "Heinz", 
        "id": "sg:person.07450173411.71", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07450173411.71"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Department of Theoretical Physics, State Pedagogical University, Str. Uly\u2019anova 1, 603600, Nizhny Novgorod, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Shondin", 
        "givenName": "Yuri", 
        "id": "sg:person.015771172577.94", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015771172577.94"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "VU University Amsterdam", 
          "id": "https://www.grid.ac/institutes/grid.12380.38", 
          "name": [
            "Department of Mathematics, Free University, De Boelelaan 1081a, 1081, HV Amsterdam, The Netherlands"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zeinstra", 
        "givenName": "Chris", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1002/mana.19851200123", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001182196"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1007624556", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-8908-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007624556", 
          "https://doi.org/10.1007/978-3-0348-8908-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-8908-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007624556", 
          "https://doi.org/10.1007/978-3-0348-8908-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-7698-8_15", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008400943", 
          "https://doi.org/10.1007/978-3-0348-7698-8_15"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-65567-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011407145", 
          "https://doi.org/10.1007/978-3-642-65567-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-65567-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011407145", 
          "https://doi.org/10.1007/978-3-642-65567-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01238863", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017336779", 
          "https://doi.org/10.1007/bf01238863"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1022022758", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-88201-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022022758", 
          "https://doi.org/10.1007/978-3-642-88201-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-88201-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022022758", 
          "https://doi.org/10.1007/978-3-642-88201-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/mana.19770770116", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027367955"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01016615", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039082334", 
          "https://doi.org/10.1007/bf01016615"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01016615", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039082334", 
          "https://doi.org/10.1007/bf01016615"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-8606-2_13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042050982", 
          "https://doi.org/10.1007/978-3-0348-8606-2_13"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-8606-2_13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042050982", 
          "https://doi.org/10.1007/978-3-0348-8606-2_13"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01017080", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052515491", 
          "https://doi.org/10.1007/bf01017080"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01017080", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052515491", 
          "https://doi.org/10.1007/bf01017080"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500009914", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054892753"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.529404", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058106419"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/pjm.1977.72.135", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069067067"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/pjm.1986.125.347", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069069157"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.5186/aasfm.1987.1208", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072648451"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/fim/003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098723787"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/mmono/017", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101567794"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/mmono/063", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101567839"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2000", 
    "datePublishedReg": "2000-01-01", 
    "description": "Let A0 be an unbounded self-adjoint operator in a Hilbert space H0 and let \u03c7 be a generalized element of order \u2014 m \u2014 1 in the rigging associated with A0 and the inner product \u3008\u00b7, \u00b7\u30090 of H0. In [S1, S2, S3] operators Ht, t \u00b7 R \u222a \u221e, are defined which serve as an interpretation for the family of operators A0 + t-1 \u3008\u00b7, \u03c7\u30090 \u03c7. The second summand here contains the inner singularity mentioned in the title. The operators Ht act in Pontryagin spaces of the form \u03c0m = H0\u2295Cm\u2295Cmwhere the direct summand space Cm \u2295 Cmis provided with an indefinite inner product. They can be interpreted both as a canonical extension of some symmetric operator S in \u03c0m and also as extensions of a one-dimensional restriction S0 of A0 in H0 and hence they can be characterized by a class of Straus extensions of S0 as well as via M.G. Krein\u2019s formulas for (generalized) resolvents. In this paper we describe both these realizations explicitly and study their spectral properties. A main role is played by a special class of Q-functions. Factorizations of these functions correspond to the separation of the nonpositive type spectrum from the positive spectrum of Ht. As a consequence, in Subsection 7.3 a family of self-adjoint Hilbert space operators is obtained which can serve as a nontrivial quantum model associated with the operators A0 + t-1 \u3008\u00b7, \u03c7\u30090 \u03c7.", 
    "editor": [
      {
        "familyName": "Adamyan", 
        "givenName": "V. M.", 
        "type": "Person"
      }, 
      {
        "familyName": "Gohberg", 
        "givenName": "I.", 
        "type": "Person"
      }, 
      {
        "familyName": "Gorbachuk", 
        "givenName": "M.", 
        "type": "Person"
      }, 
      {
        "familyName": "Gorbachuk", 
        "givenName": "V.", 
        "type": "Person"
      }, 
      {
        "familyName": "Kaashoek", 
        "givenName": "M. A.", 
        "type": "Person"
      }, 
      {
        "familyName": "Langer", 
        "givenName": "H.", 
        "type": "Person"
      }, 
      {
        "familyName": "Popov", 
        "givenName": "G.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-0348-8413-6_8", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-0348-9557-6", 
        "978-3-0348-8413-6"
      ], 
      "name": "Operator Theory and Related Topics", 
      "type": "Book"
    }, 
    "name": "Self-adjoint Operators with Inner Singularities and Pontryagin Spaces", 
    "pagination": "105-175", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1000870627"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-0348-8413-6_8"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "0425b50615652bd7835103170cdc23de7fa30d3e37d7f5da8a5e44697ba8c2fa"
        ]
      }
    ], 
    "publisher": {
      "location": "Basel", 
      "name": "Birkh\u00e4user Basel", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-0348-8413-6_8", 
      "https://app.dimensions.ai/details/publication/pub.1000870627"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T09:12", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000371_0000000371/records_130797_00000000.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-3-0348-8413-6_8"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8413-6_8'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8413-6_8'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8413-6_8'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8413-6_8'


 

This table displays all metadata directly associated to this object as RDF triples.

189 TRIPLES      23 PREDICATES      47 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-0348-8413-6_8 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nedbf24154d214524a3e23c7aeec15e83
4 schema:citation sg:pub.10.1007/978-3-0348-7698-8_15
5 sg:pub.10.1007/978-3-0348-8606-2_13
6 sg:pub.10.1007/978-3-0348-8908-7
7 sg:pub.10.1007/978-3-642-65567-8
8 sg:pub.10.1007/978-3-642-88201-2
9 sg:pub.10.1007/bf01016615
10 sg:pub.10.1007/bf01017080
11 sg:pub.10.1007/bf01238863
12 https://app.dimensions.ai/details/publication/pub.1007624556
13 https://app.dimensions.ai/details/publication/pub.1022022758
14 https://doi.org/10.1002/mana.19770770116
15 https://doi.org/10.1002/mana.19851200123
16 https://doi.org/10.1017/s0308210500009914
17 https://doi.org/10.1063/1.529404
18 https://doi.org/10.1090/fim/003
19 https://doi.org/10.1090/mmono/017
20 https://doi.org/10.1090/mmono/063
21 https://doi.org/10.2140/pjm.1977.72.135
22 https://doi.org/10.2140/pjm.1986.125.347
23 https://doi.org/10.5186/aasfm.1987.1208
24 schema:datePublished 2000
25 schema:datePublishedReg 2000-01-01
26 schema:description Let A0 be an unbounded self-adjoint operator in a Hilbert space H0 and let χ be a generalized element of order — m — 1 in the rigging associated with A0 and the inner product 〈·, ·〉0 of H0. In [S1, S2, S3] operators Ht, t · R ∪ ∞, are defined which serve as an interpretation for the family of operators A0 + t-1 〈·, χ〉0 χ. The second summand here contains the inner singularity mentioned in the title. The operators Ht act in Pontryagin spaces of the form πm = H0⊕Cm⊕Cmwhere the direct summand space Cm ⊕ Cmis provided with an indefinite inner product. They can be interpreted both as a canonical extension of some symmetric operator S in πm and also as extensions of a one-dimensional restriction S0 of A0 in H0 and hence they can be characterized by a class of Straus extensions of S0 as well as via M.G. Krein’s formulas for (generalized) resolvents. In this paper we describe both these realizations explicitly and study their spectral properties. A main role is played by a special class of Q-functions. Factorizations of these functions correspond to the separation of the nonpositive type spectrum from the positive spectrum of Ht. As a consequence, in Subsection 7.3 a family of self-adjoint Hilbert space operators is obtained which can serve as a nontrivial quantum model associated with the operators A0 + t-1 〈·, χ〉0 χ.
27 schema:editor Neb91901d198f4eb6830518e266e472d5
28 schema:genre chapter
29 schema:inLanguage en
30 schema:isAccessibleForFree false
31 schema:isPartOf Nd86d11a2fc694bdfaf00bc0b103c09ae
32 schema:name Self-adjoint Operators with Inner Singularities and Pontryagin Spaces
33 schema:pagination 105-175
34 schema:productId N76bfd03adbc44b54800af438a14b9321
35 Nf2f5bb613f0f421c9bb70cabf70d1e2a
36 Nfbfc0591b2e547319e3dad80312abab3
37 schema:publisher Nb8f1e0be950d4285a375608ba2bafc8a
38 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000870627
39 https://doi.org/10.1007/978-3-0348-8413-6_8
40 schema:sdDatePublished 2019-04-16T09:12
41 schema:sdLicense https://scigraph.springernature.com/explorer/license/
42 schema:sdPublisher N7020fbb7c3b44f93a7ba26280074f4d0
43 schema:url https://link.springer.com/10.1007%2F978-3-0348-8413-6_8
44 sgo:license sg:explorer/license/
45 sgo:sdDataset chapters
46 rdf:type schema:Chapter
47 N06484a740ace4917a9b4ca7bab523073 schema:name Department of Theoretical Physics, State Pedagogical University, Str. Uly’anova 1, 603600, Nizhny Novgorod, Russia
48 rdf:type schema:Organization
49 N0af09ebf98384b48be0c3210b61bcf7a rdf:first Na6b60efb78594c26bd31392dcd982be9
50 rdf:rest N66d00cd6fea34b93b312344b13f5f6ea
51 N0b763e12ceb544e8bc371667510fdd79 rdf:first N40869ebb432f414384ca8b9001579068
52 rdf:rest N7b9d9d1175144250a95dcbbd0e240d6a
53 N14a93cd3ea3a4692aef242c717407ca0 rdf:first sg:person.015771172577.94
54 rdf:rest N4a6592db1a1740229dd8f787c3e2c731
55 N2f1f3794563f4851b4c96e99a9efa8d6 schema:familyName Adamyan
56 schema:givenName V. M.
57 rdf:type schema:Person
58 N301ced828f644fc8be6fd1c29beefca6 rdf:first sg:person.07450173411.71
59 rdf:rest N14a93cd3ea3a4692aef242c717407ca0
60 N3d32306ab05a4c23be73d5c0943bff5f schema:affiliation https://www.grid.ac/institutes/grid.12380.38
61 schema:familyName Zeinstra
62 schema:givenName Chris
63 rdf:type schema:Person
64 N40869ebb432f414384ca8b9001579068 schema:familyName Gorbachuk
65 schema:givenName V.
66 rdf:type schema:Person
67 N4a6592db1a1740229dd8f787c3e2c731 rdf:first N3d32306ab05a4c23be73d5c0943bff5f
68 rdf:rest rdf:nil
69 N59e134ea488044b4ae4caaa234b31d73 rdf:first N9a66867d0e7b4af48a1557548f02d03b
70 rdf:rest N0b763e12ceb544e8bc371667510fdd79
71 N614c5fab1d6e402dba8044371644e147 schema:familyName Kaashoek
72 schema:givenName M. A.
73 rdf:type schema:Person
74 N66d00cd6fea34b93b312344b13f5f6ea rdf:first Nce8bafc1062e466d93e23395e2ca93fa
75 rdf:rest rdf:nil
76 N68f7574feae14cb0b099f938aafe7de1 schema:familyName Gohberg
77 schema:givenName I.
78 rdf:type schema:Person
79 N7020fbb7c3b44f93a7ba26280074f4d0 schema:name Springer Nature - SN SciGraph project
80 rdf:type schema:Organization
81 N76bfd03adbc44b54800af438a14b9321 schema:name doi
82 schema:value 10.1007/978-3-0348-8413-6_8
83 rdf:type schema:PropertyValue
84 N7b9d9d1175144250a95dcbbd0e240d6a rdf:first N614c5fab1d6e402dba8044371644e147
85 rdf:rest N0af09ebf98384b48be0c3210b61bcf7a
86 N9a66867d0e7b4af48a1557548f02d03b schema:familyName Gorbachuk
87 schema:givenName M.
88 rdf:type schema:Person
89 N9a695328e89f4929811dfaca68ec8245 rdf:first N68f7574feae14cb0b099f938aafe7de1
90 rdf:rest N59e134ea488044b4ae4caaa234b31d73
91 Na6b60efb78594c26bd31392dcd982be9 schema:familyName Langer
92 schema:givenName H.
93 rdf:type schema:Person
94 Nb8f1e0be950d4285a375608ba2bafc8a schema:location Basel
95 schema:name Birkhäuser Basel
96 rdf:type schema:Organisation
97 Nce8bafc1062e466d93e23395e2ca93fa schema:familyName Popov
98 schema:givenName G.
99 rdf:type schema:Person
100 Nd86d11a2fc694bdfaf00bc0b103c09ae schema:isbn 978-3-0348-8413-6
101 978-3-0348-9557-6
102 schema:name Operator Theory and Related Topics
103 rdf:type schema:Book
104 Neb91901d198f4eb6830518e266e472d5 rdf:first N2f1f3794563f4851b4c96e99a9efa8d6
105 rdf:rest N9a695328e89f4929811dfaca68ec8245
106 Nedbf24154d214524a3e23c7aeec15e83 rdf:first sg:person.013762723211.39
107 rdf:rest N301ced828f644fc8be6fd1c29beefca6
108 Nf2f5bb613f0f421c9bb70cabf70d1e2a schema:name readcube_id
109 schema:value 0425b50615652bd7835103170cdc23de7fa30d3e37d7f5da8a5e44697ba8c2fa
110 rdf:type schema:PropertyValue
111 Nfbfc0591b2e547319e3dad80312abab3 schema:name dimensions_id
112 schema:value pub.1000870627
113 rdf:type schema:PropertyValue
114 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
115 schema:name Mathematical Sciences
116 rdf:type schema:DefinedTerm
117 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
118 schema:name Pure Mathematics
119 rdf:type schema:DefinedTerm
120 sg:person.013762723211.39 schema:affiliation https://www.grid.ac/institutes/grid.4830.f
121 schema:familyName Dijksma
122 schema:givenName Aad
123 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013762723211.39
124 rdf:type schema:Person
125 sg:person.015771172577.94 schema:affiliation N06484a740ace4917a9b4ca7bab523073
126 schema:familyName Shondin
127 schema:givenName Yuri
128 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015771172577.94
129 rdf:type schema:Person
130 sg:person.07450173411.71 schema:affiliation https://www.grid.ac/institutes/grid.5329.d
131 schema:familyName Langer
132 schema:givenName Heinz
133 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07450173411.71
134 rdf:type schema:Person
135 sg:pub.10.1007/978-3-0348-7698-8_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008400943
136 https://doi.org/10.1007/978-3-0348-7698-8_15
137 rdf:type schema:CreativeWork
138 sg:pub.10.1007/978-3-0348-8606-2_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042050982
139 https://doi.org/10.1007/978-3-0348-8606-2_13
140 rdf:type schema:CreativeWork
141 sg:pub.10.1007/978-3-0348-8908-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007624556
142 https://doi.org/10.1007/978-3-0348-8908-7
143 rdf:type schema:CreativeWork
144 sg:pub.10.1007/978-3-642-65567-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011407145
145 https://doi.org/10.1007/978-3-642-65567-8
146 rdf:type schema:CreativeWork
147 sg:pub.10.1007/978-3-642-88201-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022022758
148 https://doi.org/10.1007/978-3-642-88201-2
149 rdf:type schema:CreativeWork
150 sg:pub.10.1007/bf01016615 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039082334
151 https://doi.org/10.1007/bf01016615
152 rdf:type schema:CreativeWork
153 sg:pub.10.1007/bf01017080 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052515491
154 https://doi.org/10.1007/bf01017080
155 rdf:type schema:CreativeWork
156 sg:pub.10.1007/bf01238863 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017336779
157 https://doi.org/10.1007/bf01238863
158 rdf:type schema:CreativeWork
159 https://app.dimensions.ai/details/publication/pub.1007624556 schema:CreativeWork
160 https://app.dimensions.ai/details/publication/pub.1022022758 schema:CreativeWork
161 https://doi.org/10.1002/mana.19770770116 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027367955
162 rdf:type schema:CreativeWork
163 https://doi.org/10.1002/mana.19851200123 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001182196
164 rdf:type schema:CreativeWork
165 https://doi.org/10.1017/s0308210500009914 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054892753
166 rdf:type schema:CreativeWork
167 https://doi.org/10.1063/1.529404 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058106419
168 rdf:type schema:CreativeWork
169 https://doi.org/10.1090/fim/003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098723787
170 rdf:type schema:CreativeWork
171 https://doi.org/10.1090/mmono/017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101567794
172 rdf:type schema:CreativeWork
173 https://doi.org/10.1090/mmono/063 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101567839
174 rdf:type schema:CreativeWork
175 https://doi.org/10.2140/pjm.1977.72.135 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069067067
176 rdf:type schema:CreativeWork
177 https://doi.org/10.2140/pjm.1986.125.347 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069069157
178 rdf:type schema:CreativeWork
179 https://doi.org/10.5186/aasfm.1987.1208 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072648451
180 rdf:type schema:CreativeWork
181 https://www.grid.ac/institutes/grid.12380.38 schema:alternateName VU University Amsterdam
182 schema:name Department of Mathematics, Free University, De Boelelaan 1081a, 1081, HV Amsterdam, The Netherlands
183 rdf:type schema:Organization
184 https://www.grid.ac/institutes/grid.4830.f schema:alternateName University of Groningen
185 schema:name Department of Mathematics, University of Groningen, P.O. Box 800, 9700, AV Groningen, The Netherlands
186 rdf:type schema:Organization
187 https://www.grid.ac/institutes/grid.5329.d schema:alternateName TU Wien
188 schema:name Department of Mathematics, Technical University of Vienna, Wiedner Haupsstrasse 8-10/1411, A-1040, Vienna, Austria
189 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...