Singular Point-like Perturbations of the Laguerre Operator in a Pontryagin Space View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2002

AUTHORS

Aad Dijksma , Yuri Shondin

ABSTRACT

The spectral problem for the Laguerre equation on (0, ∞) with real parameter a in the case 0 <|α|< 1 is closely related to the Nevanlinna \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{Q}_{\alpha }}(z) = - \pi \Gamma ( - z)/(\sin \pi \alpha )\Gamma ( - z - \alpha ). $$\end{document} function If |α| and |α|≠ 2, 3,… this function belongs to the generalized Nevanlinna class Nm, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ m = [\tfrac{{|\alpha | + 1}} {2}]. $$\end{document} A natural question appears: to what spectral problem does this function correspond? For α< -1, α ≠-2, -3,…, an answer was given by Derkach [D]. He obtained an operator representation for the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {m_\alpha }(z) = - {Q_\alpha }( - Z)/{\mathcal{T}^2}(1 + \alpha ) $$\end{document} in terms of a self-adjoint operator in a Pontryagin space and an interpretation of mα,(z) as the Titchmarsh-Weyl function of some boundary value problem related to the Laguerre equation. That an indefinite metric was needed was made clear earlier by Morton and Krall [MK]. In this note for α> 1, α ≠ 2, 3,… we answer this and related questions by using Pontryagin space operator realizations of suitable singular point-like perturbations of the Laguerre operator. We describe the operator models for Qa(z) and compare them with the models for -a. Also we discuss the spectral properties of the self-adjoint linear relations in the representation of the functions Qa(z) and -Qa(z)-1 Finally, we describe the connection between the self-adjoint linear relations in the representations of Qa(z) and Q-α (z +α) and show that this connection can be viewed as an operator implementation of the Kummer transform for confluent hypergeometric functions. More... »

PAGES

141-181

Book

TITLE

Operator Methods in Ordinary and Partial Differential Equations

ISBN

978-3-0348-9479-1
978-3-0348-8219-4

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-8219-4_13

DOI

http://dx.doi.org/10.1007/978-3-0348-8219-4_13

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020008176


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, Groningen, AV, 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": {
          "name": [
            "Department of Physics, Pedagogical State University, str. Ulyanova 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"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1006/jdeq.1999.3755", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002159253"
        ], 
        "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://doi.org/10.1002/mana.19831140116", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017905796"
        ], 
        "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/10.1006/jfan.1995.1074", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023629099"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-247x(82)90009-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023885200"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01320702", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024186821", 
          "https://doi.org/10.1007/bf01320702"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-247x(79)90090-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026702666"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/mana.19770770116", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027367955"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jfan.1995.1030", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028982361"
        ], 
        "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": "https://doi.org/10.1017/s0308210500009914", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054892753"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1664820", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057742874"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.522710", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058099730"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.527339", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058104358"
        ], 
        "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/10.1137/0509042", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062847048"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4213/mzm1311", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072366155"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/mmono/017", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101567794"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2002", 
    "datePublishedReg": "2002-01-01", 
    "description": "The spectral problem for the Laguerre equation on (0, \u221e) with real parameter a in the case 0 <|\u03b1|< 1 is closely related to the Nevanlinna \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{Q}_{\\alpha }}(z) = - \\pi \\Gamma ( - z)/(\\sin \\pi \\alpha )\\Gamma ( - z - \\alpha ). $$\\end{document} function If |\u03b1| and |\u03b1|\u2260 2, 3,\u2026 this function belongs to the generalized Nevanlinna class Nm, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ m = [\\tfrac{{|\\alpha | + 1}} {2}]. $$\\end{document} A natural question appears: to what spectral problem does this function correspond? For \u03b1< -1, \u03b1 \u2260-2, -3,\u2026, an answer was given by Derkach [D]. He obtained an operator representation for the function \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m_\\alpha }(z) = - {Q_\\alpha }( - Z)/{\\mathcal{T}^2}(1 + \\alpha ) $$\\end{document} in terms of a self-adjoint operator in a Pontryagin space and an interpretation of m\u03b1,(z) as the Titchmarsh-Weyl function of some boundary value problem related to the Laguerre equation. That an indefinite metric was needed was made clear earlier by Morton and Krall [MK]. In this note for \u03b1> 1, \u03b1 \u2260 2, 3,\u2026 we answer this and related questions by using Pontryagin space operator realizations of suitable singular point-like perturbations of the Laguerre operator. We describe the operator models for Qa(z) and compare them with the models for -a. Also we discuss the spectral properties of the self-adjoint linear relations in the representation of the functions Qa(z) and -Qa(z)-1 Finally, we describe the connection between the self-adjoint linear relations in the representations of Qa(z) and Q-\u03b1 (z +\u03b1) and show that this connection can be viewed as an operator implementation of the Kummer transform for confluent hypergeometric functions.", 
    "editor": [
      {
        "familyName": "Albeverio", 
        "givenName": "Sergio", 
        "type": "Person"
      }, 
      {
        "familyName": "Elander", 
        "givenName": "Nils", 
        "type": "Person"
      }, 
      {
        "familyName": "Everitt", 
        "givenName": "W. Norrie", 
        "type": "Person"
      }, 
      {
        "familyName": "Kurasov", 
        "givenName": "Pavel", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-0348-8219-4_13", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-0348-9479-1", 
        "978-3-0348-8219-4"
      ], 
      "name": "Operator Methods in Ordinary and Partial Differential Equations", 
      "type": "Book"
    }, 
    "name": "Singular Point-like Perturbations of the Laguerre Operator in a Pontryagin Space", 
    "pagination": "141-181", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1020008176"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-0348-8219-4_13"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "5f54efbbe1e373c4f21646163421514b68f9ff7647a52f90b50f419c1403aa88"
        ]
      }
    ], 
    "publisher": {
      "location": "Basel", 
      "name": "Birkh\u00e4user Basel", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-0348-8219-4_13", 
      "https://app.dimensions.ai/details/publication/pub.1020008176"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T09:05", 
    "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/v90/0000000370_0000000370/records_46765_00000001.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-3-0348-8219-4_13"
  }
]
 

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.10.1007/978-3-0348-8219-4_13'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8219-4_13'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8219-4_13'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8219-4_13'


 

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

152 TRIPLES      23 PREDICATES      47 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-0348-8219-4_13 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N7cf663b65e9341f8be8a3214b77eac24
4 schema:citation sg:pub.10.1007/978-3-642-88201-2
5 sg:pub.10.1007/bf01016615
6 sg:pub.10.1007/bf01238863
7 sg:pub.10.1007/bf01320702
8 https://app.dimensions.ai/details/publication/pub.1022022758
9 https://doi.org/10.1002/mana.19770770116
10 https://doi.org/10.1002/mana.19831140116
11 https://doi.org/10.1006/jdeq.1999.3755
12 https://doi.org/10.1006/jfan.1995.1030
13 https://doi.org/10.1006/jfan.1995.1074
14 https://doi.org/10.1016/0022-247x(79)90090-8
15 https://doi.org/10.1016/0022-247x(82)90009-9
16 https://doi.org/10.1017/s0308210500009914
17 https://doi.org/10.1063/1.1664820
18 https://doi.org/10.1063/1.522710
19 https://doi.org/10.1063/1.527339
20 https://doi.org/10.1063/1.529404
21 https://doi.org/10.1090/mmono/017
22 https://doi.org/10.1137/0509042
23 https://doi.org/10.4213/mzm1311
24 schema:datePublished 2002
25 schema:datePublishedReg 2002-01-01
26 schema:description The spectral problem for the Laguerre equation on (0, ∞) with real parameter a in the case 0 <|α|< 1 is closely related to the Nevanlinna \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{Q}_{\alpha }}(z) = - \pi \Gamma ( - z)/(\sin \pi \alpha )\Gamma ( - z - \alpha ). $$\end{document} function If |α| and |α|≠ 2, 3,… this function belongs to the generalized Nevanlinna class Nm, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ m = [\tfrac{{|\alpha | + 1}} {2}]. $$\end{document} A natural question appears: to what spectral problem does this function correspond? For α< -1, α ≠-2, -3,…, an answer was given by Derkach [D]. He obtained an operator representation for the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {m_\alpha }(z) = - {Q_\alpha }( - Z)/{\mathcal{T}^2}(1 + \alpha ) $$\end{document} in terms of a self-adjoint operator in a Pontryagin space and an interpretation of mα,(z) as the Titchmarsh-Weyl function of some boundary value problem related to the Laguerre equation. That an indefinite metric was needed was made clear earlier by Morton and Krall [MK]. In this note for α> 1, α ≠ 2, 3,… we answer this and related questions by using Pontryagin space operator realizations of suitable singular point-like perturbations of the Laguerre operator. We describe the operator models for Qa(z) and compare them with the models for -a. Also we discuss the spectral properties of the self-adjoint linear relations in the representation of the functions Qa(z) and -Qa(z)-1 Finally, we describe the connection between the self-adjoint linear relations in the representations of Qa(z) and Q-α (z +α) and show that this connection can be viewed as an operator implementation of the Kummer transform for confluent hypergeometric functions.
27 schema:editor Nc9f84100d2b24323965974601b8d1bcf
28 schema:genre chapter
29 schema:inLanguage en
30 schema:isAccessibleForFree false
31 schema:isPartOf N3c047ca01f9b4b5e84a9f1cfcdd1303f
32 schema:name Singular Point-like Perturbations of the Laguerre Operator in a Pontryagin Space
33 schema:pagination 141-181
34 schema:productId N4de0e6c4dd224fa4a0066e0fe48f5ea4
35 N8df0bdcdc09945db8460518c91d9893e
36 Nd9ef19c4891947c3a0fd415f8ea6f643
37 schema:publisher Ne7d21bf6b60f4d5b8b298246fd5eb26c
38 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020008176
39 https://doi.org/10.1007/978-3-0348-8219-4_13
40 schema:sdDatePublished 2019-04-16T09:05
41 schema:sdLicense https://scigraph.springernature.com/explorer/license/
42 schema:sdPublisher N8d69d1efb72c4a6fbbe690a44872a2cf
43 schema:url https://link.springer.com/10.1007%2F978-3-0348-8219-4_13
44 sgo:license sg:explorer/license/
45 sgo:sdDataset chapters
46 rdf:type schema:Chapter
47 N02f609b849054185a396884de32cab28 schema:name Department of Physics, Pedagogical State University, str. Ulyanova 1, 603600, Nizhny Novgorod, Russia
48 rdf:type schema:Organization
49 N050b629a710a4b5aa64d306d86b03ef2 schema:familyName Albeverio
50 schema:givenName Sergio
51 rdf:type schema:Person
52 N3c047ca01f9b4b5e84a9f1cfcdd1303f schema:isbn 978-3-0348-8219-4
53 978-3-0348-9479-1
54 schema:name Operator Methods in Ordinary and Partial Differential Equations
55 rdf:type schema:Book
56 N4de0e6c4dd224fa4a0066e0fe48f5ea4 schema:name dimensions_id
57 schema:value pub.1020008176
58 rdf:type schema:PropertyValue
59 N7942d588e58d48fd9d4bb07b9c77f7dd rdf:first Nafa4157d8b3448349e8c439afb5219b0
60 rdf:rest Na9d7d36eb1d342b6a4761d41254286bd
61 N7cf663b65e9341f8be8a3214b77eac24 rdf:first sg:person.013762723211.39
62 rdf:rest N941f464cefea473182b036191e499f48
63 N8b29c5ac812a40e5bd153ff19aa44e95 schema:familyName Kurasov
64 schema:givenName Pavel
65 rdf:type schema:Person
66 N8d69d1efb72c4a6fbbe690a44872a2cf schema:name Springer Nature - SN SciGraph project
67 rdf:type schema:Organization
68 N8df0bdcdc09945db8460518c91d9893e schema:name doi
69 schema:value 10.1007/978-3-0348-8219-4_13
70 rdf:type schema:PropertyValue
71 N941f464cefea473182b036191e499f48 rdf:first sg:person.015771172577.94
72 rdf:rest rdf:nil
73 Na9d7d36eb1d342b6a4761d41254286bd rdf:first Nc4e10cef86df44cab898cac90cfc8bc7
74 rdf:rest Ndbdd6a2778a141e7a902f00686da4a51
75 Nafa4157d8b3448349e8c439afb5219b0 schema:familyName Elander
76 schema:givenName Nils
77 rdf:type schema:Person
78 Nc4e10cef86df44cab898cac90cfc8bc7 schema:familyName Everitt
79 schema:givenName W. Norrie
80 rdf:type schema:Person
81 Nc9f84100d2b24323965974601b8d1bcf rdf:first N050b629a710a4b5aa64d306d86b03ef2
82 rdf:rest N7942d588e58d48fd9d4bb07b9c77f7dd
83 Nd9ef19c4891947c3a0fd415f8ea6f643 schema:name readcube_id
84 schema:value 5f54efbbe1e373c4f21646163421514b68f9ff7647a52f90b50f419c1403aa88
85 rdf:type schema:PropertyValue
86 Ndbdd6a2778a141e7a902f00686da4a51 rdf:first N8b29c5ac812a40e5bd153ff19aa44e95
87 rdf:rest rdf:nil
88 Ne7d21bf6b60f4d5b8b298246fd5eb26c schema:location Basel
89 schema:name Birkhäuser Basel
90 rdf:type schema:Organisation
91 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
92 schema:name Mathematical Sciences
93 rdf:type schema:DefinedTerm
94 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
95 schema:name Pure Mathematics
96 rdf:type schema:DefinedTerm
97 sg:person.013762723211.39 schema:affiliation https://www.grid.ac/institutes/grid.4830.f
98 schema:familyName Dijksma
99 schema:givenName Aad
100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013762723211.39
101 rdf:type schema:Person
102 sg:person.015771172577.94 schema:affiliation N02f609b849054185a396884de32cab28
103 schema:familyName Shondin
104 schema:givenName Yuri
105 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015771172577.94
106 rdf:type schema:Person
107 sg:pub.10.1007/978-3-642-88201-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022022758
108 https://doi.org/10.1007/978-3-642-88201-2
109 rdf:type schema:CreativeWork
110 sg:pub.10.1007/bf01016615 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039082334
111 https://doi.org/10.1007/bf01016615
112 rdf:type schema:CreativeWork
113 sg:pub.10.1007/bf01238863 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017336779
114 https://doi.org/10.1007/bf01238863
115 rdf:type schema:CreativeWork
116 sg:pub.10.1007/bf01320702 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024186821
117 https://doi.org/10.1007/bf01320702
118 rdf:type schema:CreativeWork
119 https://app.dimensions.ai/details/publication/pub.1022022758 schema:CreativeWork
120 https://doi.org/10.1002/mana.19770770116 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027367955
121 rdf:type schema:CreativeWork
122 https://doi.org/10.1002/mana.19831140116 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017905796
123 rdf:type schema:CreativeWork
124 https://doi.org/10.1006/jdeq.1999.3755 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002159253
125 rdf:type schema:CreativeWork
126 https://doi.org/10.1006/jfan.1995.1030 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028982361
127 rdf:type schema:CreativeWork
128 https://doi.org/10.1006/jfan.1995.1074 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023629099
129 rdf:type schema:CreativeWork
130 https://doi.org/10.1016/0022-247x(79)90090-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026702666
131 rdf:type schema:CreativeWork
132 https://doi.org/10.1016/0022-247x(82)90009-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023885200
133 rdf:type schema:CreativeWork
134 https://doi.org/10.1017/s0308210500009914 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054892753
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1063/1.1664820 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057742874
137 rdf:type schema:CreativeWork
138 https://doi.org/10.1063/1.522710 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058099730
139 rdf:type schema:CreativeWork
140 https://doi.org/10.1063/1.527339 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058104358
141 rdf:type schema:CreativeWork
142 https://doi.org/10.1063/1.529404 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058106419
143 rdf:type schema:CreativeWork
144 https://doi.org/10.1090/mmono/017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101567794
145 rdf:type schema:CreativeWork
146 https://doi.org/10.1137/0509042 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062847048
147 rdf:type schema:CreativeWork
148 https://doi.org/10.4213/mzm1311 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072366155
149 rdf:type schema:CreativeWork
150 https://www.grid.ac/institutes/grid.4830.f schema:alternateName University of Groningen
151 schema:name Department of Mathematics, University of Groningen, P. O. Box 800, 9700, Groningen, AV, The Netherlands
152 rdf:type schema:Organization
 




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


...