Ontology type: schema:Chapter
2000
AUTHORSDaniel Alpay , Aad Dijksma , Heinz Langer
ABSTRACTWe 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... »
PAGES1-50
Operator Theory and Interpolation
ISBN
978-3-0348-9560-6
978-3-0348-8422-8
http://scigraph.springernature.com/pub.10.1007/978-3-0348-8422-8_1
DOIhttp://dx.doi.org/10.1007/978-3-0348-8422-8_1
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1027404163
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
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