Classical Nevanlinna-Pick Interpolation with Real Interpolation Points View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2000

AUTHORS

Daniel Alpay , Aad Dijksma , Heinz Langer

ABSTRACT

We consider a scalar Nevanlinna-Pick interpolation problem with at most countably many interpolation points which lie in ℂ+ ∪ ℝ. Questions about the existence and uniqueness of the solutions are considered. In the case of nonuniqueness a description of all solutions is given which generalizes Potapov’s formula. Our results are obtained in two ways: in Sections 1–5 through the theory of selfadjoint extensions of a symmetric relation in a Hilbert space, including Krein’s formula and the socalled u-resolvent matrix, and in Sections 6 and 7 via the theory of reproducing kernel Hilbert spaces. More... »

PAGES

1-50

Book

TITLE

Operator Theory and Interpolation

ISBN

978-3-0348-9560-6
978-3-0348-8422-8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-8422-8_1

DOI

http://dx.doi.org/10.1007/978-3-0348-8422-8_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1027404163


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": "Ben-Gurion University of the Negev", 
          "id": "https://www.grid.ac/institutes/grid.7489.2", 
          "name": [
            "Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Alpay", 
        "givenName": "Daniel", 
        "id": "sg:person.011517101346.40", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011517101346.40"
        ], 
        "type": "Person"
      }, 
      {
        "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 Hauptstrasse 8-10, 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"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/0024-3795(95)00700-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004531712"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02559538", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009068199", 
          "https://doi.org/10.1007/bf02559538"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02786620", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023301271", 
          "https://doi.org/10.1007/bf02786620"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02786620", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023301271", 
          "https://doi.org/10.1007/bf02786620"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-1236(78)90064-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035417758"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01200325", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039094925", 
          "https://doi.org/10.1007/bf01200325"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-5672-0_3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042293429", 
          "https://doi.org/10.1007/978-3-0348-5672-0_3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1043632982", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-7709-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043632982", 
          "https://doi.org/10.1007/978-3-0348-7709-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-7709-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043632982", 
          "https://doi.org/10.1007/978-3-0348-7709-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02020526", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053174114", 
          "https://doi.org/10.1007/bf02020526"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02020526", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053174114", 
          "https://doi.org/10.1007/bf02020526"
        ], 
        "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/10.1090/trans2/097/06", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089183841"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/cbms/071", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098722335"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2000", 
    "datePublishedReg": "2000-01-01", 
    "description": "We consider a scalar Nevanlinna-Pick interpolation problem with at most countably many interpolation points which lie in \u2102+ \u222a \u211d. Questions about the existence and uniqueness of the solutions are considered. In the case of nonuniqueness a description of all solutions is given which generalizes Potapov\u2019s formula. Our results are obtained in two ways: in Sections 1\u20135 through the theory of selfadjoint extensions of a symmetric relation in a Hilbert space, including Krein\u2019s formula and the socalled u-resolvent matrix, and in Sections 6 and 7 via the theory of reproducing kernel Hilbert spaces.", 
    "editor": [
      {
        "familyName": "Bercovici", 
        "givenName": "Hari", 
        "type": "Person"
      }, 
      {
        "familyName": "Foias", 
        "givenName": "Ciprian I.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-0348-8422-8_1", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-0348-9560-6", 
        "978-3-0348-8422-8"
      ], 
      "name": "Operator Theory and Interpolation", 
      "type": "Book"
    }, 
    "name": "Classical Nevanlinna-Pick Interpolation with Real Interpolation Points", 
    "pagination": "1-50", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1027404163"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-0348-8422-8_1"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "828b483e20a17acc55bb7d400121dd5d12d5e9e060d8f75442772d110632906e"
        ]
      }
    ], 
    "publisher": {
      "location": "Basel", 
      "name": "Birkh\u00e4user Basel", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-0348-8422-8_1", 
      "https://app.dimensions.ai/details/publication/pub.1027404163"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T08:46", 
    "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/v90/0000000367_0000000367/records_88236_00000000.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-3-0348-8422-8_1"
  }
]
 

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.10.1007/978-3-0348-8422-8_1'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8422-8_1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8422-8_1'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-8422-8_1'


 

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

131 TRIPLES      23 PREDICATES      39 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-0348-8422-8_1 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N1f1d80933f134d7fbab8d4720c2dd372
4 schema:citation sg:pub.10.1007/978-3-0348-5672-0_3
5 sg:pub.10.1007/978-3-0348-7709-1
6 sg:pub.10.1007/bf01200325
7 sg:pub.10.1007/bf02020526
8 sg:pub.10.1007/bf02559538
9 sg:pub.10.1007/bf02786620
10 https://app.dimensions.ai/details/publication/pub.1043632982
11 https://doi.org/10.1016/0022-1236(78)90064-2
12 https://doi.org/10.1016/0024-3795(95)00700-8
13 https://doi.org/10.1090/cbms/071
14 https://doi.org/10.1090/trans2/097/06
15 https://doi.org/10.2140/pjm.1977.72.135
16 schema:datePublished 2000
17 schema:datePublishedReg 2000-01-01
18 schema:description We consider a scalar Nevanlinna-Pick interpolation problem with at most countably many interpolation points which lie in ℂ+ ∪ ℝ. Questions about the existence and uniqueness of the solutions are considered. In the case of nonuniqueness a description of all solutions is given which generalizes Potapov’s formula. Our results are obtained in two ways: in Sections 1–5 through the theory of selfadjoint extensions of a symmetric relation in a Hilbert space, including Krein’s formula and the socalled u-resolvent matrix, and in Sections 6 and 7 via the theory of reproducing kernel Hilbert spaces.
19 schema:editor N8af92c75e2614587afad0373895bd70c
20 schema:genre chapter
21 schema:inLanguage en
22 schema:isAccessibleForFree false
23 schema:isPartOf N6f0b69a588a142c18cc792aa71f57833
24 schema:name Classical Nevanlinna-Pick Interpolation with Real Interpolation Points
25 schema:pagination 1-50
26 schema:productId N58b695f4a0284407a65f9c7b35602510
27 N9bd953a45ed74f58b7fcce47680e5b1a
28 Nebab85d457854f84849c406b9b71d2d1
29 schema:publisher N32d0e1b0b6df4e25a9f7426ccf8d6132
30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027404163
31 https://doi.org/10.1007/978-3-0348-8422-8_1
32 schema:sdDatePublished 2019-04-16T08:46
33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
34 schema:sdPublisher N03e026e8da1247fbab8ca4bb6e0035c2
35 schema:url https://link.springer.com/10.1007%2F978-3-0348-8422-8_1
36 sgo:license sg:explorer/license/
37 sgo:sdDataset chapters
38 rdf:type schema:Chapter
39 N03e026e8da1247fbab8ca4bb6e0035c2 schema:name Springer Nature - SN SciGraph project
40 rdf:type schema:Organization
41 N1f1d80933f134d7fbab8d4720c2dd372 rdf:first sg:person.011517101346.40
42 rdf:rest N5d6c03ae9edd4785a012304fa982f1d7
43 N2b549b6ec3194d52b4f941dfa94f4bae schema:familyName Foias
44 schema:givenName Ciprian I.
45 rdf:type schema:Person
46 N32d0e1b0b6df4e25a9f7426ccf8d6132 schema:location Basel
47 schema:name Birkhäuser Basel
48 rdf:type schema:Organisation
49 N3e3038414e444a26a3d74d08e1746179 schema:familyName Bercovici
50 schema:givenName Hari
51 rdf:type schema:Person
52 N58b695f4a0284407a65f9c7b35602510 schema:name dimensions_id
53 schema:value pub.1027404163
54 rdf:type schema:PropertyValue
55 N5d6c03ae9edd4785a012304fa982f1d7 rdf:first sg:person.013762723211.39
56 rdf:rest N5f7a202871644a0a93a1afe67d2a66a9
57 N5f7a202871644a0a93a1afe67d2a66a9 rdf:first sg:person.07450173411.71
58 rdf:rest rdf:nil
59 N6f0b69a588a142c18cc792aa71f57833 schema:isbn 978-3-0348-8422-8
60 978-3-0348-9560-6
61 schema:name Operator Theory and Interpolation
62 rdf:type schema:Book
63 N8af92c75e2614587afad0373895bd70c rdf:first N3e3038414e444a26a3d74d08e1746179
64 rdf:rest N9ae99d84bc5841e393ef521850332875
65 N9ae99d84bc5841e393ef521850332875 rdf:first N2b549b6ec3194d52b4f941dfa94f4bae
66 rdf:rest rdf:nil
67 N9bd953a45ed74f58b7fcce47680e5b1a schema:name doi
68 schema:value 10.1007/978-3-0348-8422-8_1
69 rdf:type schema:PropertyValue
70 Nebab85d457854f84849c406b9b71d2d1 schema:name readcube_id
71 schema:value 828b483e20a17acc55bb7d400121dd5d12d5e9e060d8f75442772d110632906e
72 rdf:type schema:PropertyValue
73 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
74 schema:name Mathematical Sciences
75 rdf:type schema:DefinedTerm
76 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
77 schema:name Pure Mathematics
78 rdf:type schema:DefinedTerm
79 sg:person.011517101346.40 schema:affiliation https://www.grid.ac/institutes/grid.7489.2
80 schema:familyName Alpay
81 schema:givenName Daniel
82 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011517101346.40
83 rdf:type schema:Person
84 sg:person.013762723211.39 schema:affiliation https://www.grid.ac/institutes/grid.4830.f
85 schema:familyName Dijksma
86 schema:givenName Aad
87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013762723211.39
88 rdf:type schema:Person
89 sg:person.07450173411.71 schema:affiliation https://www.grid.ac/institutes/grid.5329.d
90 schema:familyName Langer
91 schema:givenName Heinz
92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07450173411.71
93 rdf:type schema:Person
94 sg:pub.10.1007/978-3-0348-5672-0_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042293429
95 https://doi.org/10.1007/978-3-0348-5672-0_3
96 rdf:type schema:CreativeWork
97 sg:pub.10.1007/978-3-0348-7709-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043632982
98 https://doi.org/10.1007/978-3-0348-7709-1
99 rdf:type schema:CreativeWork
100 sg:pub.10.1007/bf01200325 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039094925
101 https://doi.org/10.1007/bf01200325
102 rdf:type schema:CreativeWork
103 sg:pub.10.1007/bf02020526 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053174114
104 https://doi.org/10.1007/bf02020526
105 rdf:type schema:CreativeWork
106 sg:pub.10.1007/bf02559538 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009068199
107 https://doi.org/10.1007/bf02559538
108 rdf:type schema:CreativeWork
109 sg:pub.10.1007/bf02786620 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023301271
110 https://doi.org/10.1007/bf02786620
111 rdf:type schema:CreativeWork
112 https://app.dimensions.ai/details/publication/pub.1043632982 schema:CreativeWork
113 https://doi.org/10.1016/0022-1236(78)90064-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035417758
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1016/0024-3795(95)00700-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004531712
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1090/cbms/071 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098722335
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1090/trans2/097/06 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089183841
120 rdf:type schema:CreativeWork
121 https://doi.org/10.2140/pjm.1977.72.135 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069067067
122 rdf:type schema:CreativeWork
123 https://www.grid.ac/institutes/grid.4830.f schema:alternateName University of Groningen
124 schema:name Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands
125 rdf:type schema:Organization
126 https://www.grid.ac/institutes/grid.5329.d schema:alternateName TU Wien
127 schema:name Department of Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria
128 rdf:type schema:Organization
129 https://www.grid.ac/institutes/grid.7489.2 schema:alternateName Ben-Gurion University of the Negev
130 schema:name Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel
131 rdf:type schema:Organization
 




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


...