Approximation of Nκ∞-functions I: Models and Regularization View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2008

AUTHORS

Aad Dijksma , Annemarie Luger , Yuri Shondin

ABSTRACT

The class Ngk∞ consists of all generalized Nevanlinna functions N with κ negative squares for which the root space at ∞ of the self-adjoint relation in the minimal model (short for self-adjoint operator realization) of N contains a κ-dimensional non-positive subspace. In this paper we discuss two specific models for the function N ∈ Ngk∞: one associated with the irreducible representation of N and one associated with a regularized version of this representation which need not be irreducible. The state space in each of these models is a reproducing kernel Pontryagin space whose reproducing kernel is a matrix function constructed from the data in the representation. More... »

PAGES

87-112

Book

TITLE

Spectral Theory in Inner Product Spaces and Applications

ISBN

978-3-7643-8910-9
978-3-7643-8911-6

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-7643-8911-6_5

DOI

http://dx.doi.org/10.1007/978-3-7643-8911-6_5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1024574044


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 407, 9700, AK 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": "Lund University", 
          "id": "https://www.grid.ac/institutes/grid.4514.4", 
          "name": [
            "Department of Mathematics, Lund Institute of Technology, Box 118, SE-221 00, Lund, Sweden"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Luger", 
        "givenName": "Annemarie", 
        "id": "sg:person.011442625430.95", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011442625430.95"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Department of theoretical Physics, State Pedagogical University, GSP 37, Str. Ulyanova 1, 603950, 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": "sg:pub.10.1007/978-3-0348-8413-6_8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000870627", 
          "https://doi.org/10.1007/978-3-0348-8413-6_8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-8413-6_8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000870627", 
          "https://doi.org/10.1007/978-3-0348-8413-6_8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jdeq.1999.3755", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002159253"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-7698-8_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/bf01349967", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009365586", 
          "https://doi.org/10.1007/bf01349967"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-12678-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011943444", 
          "https://doi.org/10.1007/978-3-662-12678-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-12678-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011943444", 
          "https://doi.org/10.1007/978-3-662-12678-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0022-1236(03)00068-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017222504"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0022-1236(03)00068-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017222504"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2003.06.005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020692391"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-7947-7_5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021766530", 
          "https://doi.org/10.1007/978-3-0348-7947-7_5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-7947-7_5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021766530", 
          "https://doi.org/10.1007/978-3-0348-7947-7_5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/mana.19931610110", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025837130"
        ], 
        "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/10.1088/0305-4470/38/22/023", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059079223"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0305-4470/38/22/023", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059079223"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/trans2/103/01", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089181772"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2008", 
    "datePublishedReg": "2008-01-01", 
    "description": "The class Ngk\u221e consists of all generalized Nevanlinna functions N with \u03ba negative squares for which the root space at \u221e of the self-adjoint relation in the minimal model (short for self-adjoint operator realization) of N contains a \u03ba-dimensional non-positive subspace. In this paper we discuss two specific models for the function N \u2208 Ngk\u221e: one associated with the irreducible representation of N and one associated with a regularized version of this representation which need not be irreducible. The state space in each of these models is a reproducing kernel Pontryagin space whose reproducing kernel is a matrix function constructed from the data in the representation.", 
    "editor": [
      {
        "familyName": "Behrndt", 
        "givenName": "Jussi", 
        "type": "Person"
      }, 
      {
        "familyName": "F\u00f6rster", 
        "givenName": "Karl-Heinz", 
        "type": "Person"
      }, 
      {
        "familyName": "Langer", 
        "givenName": "Heinz", 
        "type": "Person"
      }, 
      {
        "familyName": "Trunk", 
        "givenName": "Carsten", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-7643-8911-6_5", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-7643-8910-9", 
        "978-3-7643-8911-6"
      ], 
      "name": "Spectral Theory in Inner Product Spaces and Applications", 
      "type": "Book"
    }, 
    "name": "Approximation of N\u03ba\u221e-functions I: Models and Regularization", 
    "pagination": "87-112", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-7643-8911-6_5"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "75122b2e9a04976beeb5c7bf083a5f4618f33bf095fe00605c95a1c491f76959"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1024574044"
        ]
      }
    ], 
    "publisher": {
      "location": "Basel", 
      "name": "Birkh\u00e4user Basel", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-7643-8911-6_5", 
      "https://app.dimensions.ai/details/publication/pub.1024574044"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T06:16", 
    "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/v90/0000000351_0000000351/records_43266_00000000.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-3-7643-8911-6_5"
  }
]
 

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.10.1007/978-3-7643-8911-6_5'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-7643-8911-6_5'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-7643-8911-6_5'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-7643-8911-6_5'


 

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

140 TRIPLES      23 PREDICATES      39 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-7643-8911-6_5 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N7b29dbb91b564b86a434783c6a793bb2
4 schema:citation sg:pub.10.1007/978-3-0348-7698-8_15
5 sg:pub.10.1007/978-3-0348-7947-7_5
6 sg:pub.10.1007/978-3-0348-8413-6_8
7 sg:pub.10.1007/978-3-662-12678-3
8 sg:pub.10.1007/bf01349967
9 https://doi.org/10.1002/mana.19770770116
10 https://doi.org/10.1002/mana.19931610110
11 https://doi.org/10.1006/jdeq.1999.3755
12 https://doi.org/10.1016/j.jfa.2003.06.005
13 https://doi.org/10.1016/s0022-1236(03)00068-5
14 https://doi.org/10.1088/0305-4470/38/22/023
15 https://doi.org/10.1090/trans2/103/01
16 schema:datePublished 2008
17 schema:datePublishedReg 2008-01-01
18 schema:description The class Ngk∞ consists of all generalized Nevanlinna functions N with κ negative squares for which the root space at ∞ of the self-adjoint relation in the minimal model (short for self-adjoint operator realization) of N contains a κ-dimensional non-positive subspace. In this paper we discuss two specific models for the function N ∈ Ngk∞: one associated with the irreducible representation of N and one associated with a regularized version of this representation which need not be irreducible. The state space in each of these models is a reproducing kernel Pontryagin space whose reproducing kernel is a matrix function constructed from the data in the representation.
19 schema:editor Ne576def3f8cd46a1810fe5b9ce8851ea
20 schema:genre chapter
21 schema:inLanguage en
22 schema:isAccessibleForFree false
23 schema:isPartOf N8843c7d7f2094d1f9fe2b92cc5cd7208
24 schema:name Approximation of Nκ∞-functions I: Models and Regularization
25 schema:pagination 87-112
26 schema:productId N0f6f0410ff224f42bca00d9533529fd2
27 N3edc87e5096248948ce72c97d3fdc8a4
28 Nc0249b5ee14a4881b8417d7ce5131efa
29 schema:publisher Nb66243617fe54a35b45a745b18e3eb67
30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024574044
31 https://doi.org/10.1007/978-3-7643-8911-6_5
32 schema:sdDatePublished 2019-04-16T06:16
33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
34 schema:sdPublisher N33ec2b5fbce0432d9b61a70d54c70d76
35 schema:url https://link.springer.com/10.1007%2F978-3-7643-8911-6_5
36 sgo:license sg:explorer/license/
37 sgo:sdDataset chapters
38 rdf:type schema:Chapter
39 N0ec5935d8bce4a66a7aa155bee6c2fe2 schema:name Department of theoretical Physics, State Pedagogical University, GSP 37, Str. Ulyanova 1, 603950, Nizhny Novgorod, Russia
40 rdf:type schema:Organization
41 N0f3f7f8b805948c5ba3792ad7edd6d40 rdf:first sg:person.015771172577.94
42 rdf:rest rdf:nil
43 N0f6f0410ff224f42bca00d9533529fd2 schema:name dimensions_id
44 schema:value pub.1024574044
45 rdf:type schema:PropertyValue
46 N33ec2b5fbce0432d9b61a70d54c70d76 schema:name Springer Nature - SN SciGraph project
47 rdf:type schema:Organization
48 N3edc87e5096248948ce72c97d3fdc8a4 schema:name readcube_id
49 schema:value 75122b2e9a04976beeb5c7bf083a5f4618f33bf095fe00605c95a1c491f76959
50 rdf:type schema:PropertyValue
51 N6256c7d901e54c5b80d5f97626df45a4 schema:familyName Behrndt
52 schema:givenName Jussi
53 rdf:type schema:Person
54 N631fe9550fe34b9785b752980100e4f2 rdf:first sg:person.011442625430.95
55 rdf:rest N0f3f7f8b805948c5ba3792ad7edd6d40
56 N67ffa64ece8447078ba0924dc8d3d5da schema:familyName Trunk
57 schema:givenName Carsten
58 rdf:type schema:Person
59 N7b29dbb91b564b86a434783c6a793bb2 rdf:first sg:person.013762723211.39
60 rdf:rest N631fe9550fe34b9785b752980100e4f2
61 N8843c7d7f2094d1f9fe2b92cc5cd7208 schema:isbn 978-3-7643-8910-9
62 978-3-7643-8911-6
63 schema:name Spectral Theory in Inner Product Spaces and Applications
64 rdf:type schema:Book
65 N8d7d38995df74797a00565726acf0f66 rdf:first N67ffa64ece8447078ba0924dc8d3d5da
66 rdf:rest rdf:nil
67 N8ddd7d139b3b4a4bb6ab3775adb68291 rdf:first Neacbe4f53a6b4a7998c5bf063f12f282
68 rdf:rest Nddd25e05290b43f891ca1faa2d7c78b7
69 Nb66243617fe54a35b45a745b18e3eb67 schema:location Basel
70 schema:name Birkhäuser Basel
71 rdf:type schema:Organisation
72 Nc0249b5ee14a4881b8417d7ce5131efa schema:name doi
73 schema:value 10.1007/978-3-7643-8911-6_5
74 rdf:type schema:PropertyValue
75 Nddd25e05290b43f891ca1faa2d7c78b7 rdf:first Ne8bfe0a29d23434dadce6aa493100343
76 rdf:rest N8d7d38995df74797a00565726acf0f66
77 Ne576def3f8cd46a1810fe5b9ce8851ea rdf:first N6256c7d901e54c5b80d5f97626df45a4
78 rdf:rest N8ddd7d139b3b4a4bb6ab3775adb68291
79 Ne8bfe0a29d23434dadce6aa493100343 schema:familyName Langer
80 schema:givenName Heinz
81 rdf:type schema:Person
82 Neacbe4f53a6b4a7998c5bf063f12f282 schema:familyName Förster
83 schema:givenName Karl-Heinz
84 rdf:type schema:Person
85 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
86 schema:name Mathematical Sciences
87 rdf:type schema:DefinedTerm
88 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
89 schema:name Pure Mathematics
90 rdf:type schema:DefinedTerm
91 sg:person.011442625430.95 schema:affiliation https://www.grid.ac/institutes/grid.4514.4
92 schema:familyName Luger
93 schema:givenName Annemarie
94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011442625430.95
95 rdf:type schema:Person
96 sg:person.013762723211.39 schema:affiliation https://www.grid.ac/institutes/grid.4830.f
97 schema:familyName Dijksma
98 schema:givenName Aad
99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013762723211.39
100 rdf:type schema:Person
101 sg:person.015771172577.94 schema:affiliation N0ec5935d8bce4a66a7aa155bee6c2fe2
102 schema:familyName Shondin
103 schema:givenName Yuri
104 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015771172577.94
105 rdf:type schema:Person
106 sg:pub.10.1007/978-3-0348-7698-8_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008400943
107 https://doi.org/10.1007/978-3-0348-7698-8_15
108 rdf:type schema:CreativeWork
109 sg:pub.10.1007/978-3-0348-7947-7_5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021766530
110 https://doi.org/10.1007/978-3-0348-7947-7_5
111 rdf:type schema:CreativeWork
112 sg:pub.10.1007/978-3-0348-8413-6_8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000870627
113 https://doi.org/10.1007/978-3-0348-8413-6_8
114 rdf:type schema:CreativeWork
115 sg:pub.10.1007/978-3-662-12678-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011943444
116 https://doi.org/10.1007/978-3-662-12678-3
117 rdf:type schema:CreativeWork
118 sg:pub.10.1007/bf01349967 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009365586
119 https://doi.org/10.1007/bf01349967
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1002/mana.19770770116 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027367955
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1002/mana.19931610110 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025837130
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1006/jdeq.1999.3755 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002159253
126 rdf:type schema:CreativeWork
127 https://doi.org/10.1016/j.jfa.2003.06.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020692391
128 rdf:type schema:CreativeWork
129 https://doi.org/10.1016/s0022-1236(03)00068-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017222504
130 rdf:type schema:CreativeWork
131 https://doi.org/10.1088/0305-4470/38/22/023 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059079223
132 rdf:type schema:CreativeWork
133 https://doi.org/10.1090/trans2/103/01 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089181772
134 rdf:type schema:CreativeWork
135 https://www.grid.ac/institutes/grid.4514.4 schema:alternateName Lund University
136 schema:name Department of Mathematics, Lund Institute of Technology, Box 118, SE-221 00, Lund, Sweden
137 rdf:type schema:Organization
138 https://www.grid.ac/institutes/grid.4830.f schema:alternateName University of Groningen
139 schema:name Department of Mathematics, University of Groningen, P.O. Box 407, 9700, AK Groningen, The Netherlands
140 rdf:type schema:Organization
 




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


...