Ontology type: schema:Chapter Open Access: True
2006
AUTHORSDaniel Alpay , Aad Dijksma , Heinz Langer , Gerald Wanjala
ABSTRACTWe define and solve a boundary interpolation problem for generalized Schur functions s(z) on the open unit disk \( \mathbb{D}\) which have preassigned asymptotics when z from \( \mathbb{D}\) tends nontangentially to a boundary point z 1 ∈ \( \mathbb{T}\). The solutions are characterized via a fractional linear parametrization formula. We also prove that a rational J-unitary 2 × 2-matrix function whose only pole is at z 1 has a unique minimal factorization into elementary factors and we classify these factors. The parametrization formula is then used in an algorithm for obtaining this factorization. In the proofs we use reproducing kernel space methods. More... »
PAGES1-29
Interpolation, Schur Functions and Moment Problems
ISBN3-7643-7546-9
http://scigraph.springernature.com/pub.10.1007/3-7643-7547-7_1
DOIhttp://dx.doi.org/10.1007/3-7643-7547-7_1
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1002676549
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, Beer-Sheva, 84105, 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, NL-9700 AV\u00a0Groningen, 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": [
"Institute of Analysis and Computational Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040\u00a0Vienna, 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": {
"alternateName": "Mbarara University of Science and Technology",
"id": "https://www.grid.ac/institutes/grid.33440.30",
"name": [
"Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410, Mbarara, Uganda"
],
"type": "Organization"
},
"familyName": "Wanjala",
"givenName": "Gerald",
"id": "sg:person.012754335703.52",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012754335703.52"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/bf01204261",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1001047275",
"https://doi.org/10.1007/bf01204261"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-247x(75)90093-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1011894065"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01691925",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019968975",
"https://doi.org/10.1007/bf01691925"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01691925",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019968975",
"https://doi.org/10.1007/bf01691925"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01691925",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019968975",
"https://doi.org/10.1007/bf01691925"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.laa.2004.02.037",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1031956638"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01238220",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1033101609",
"https://doi.org/10.1007/bf01238220"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01238220",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1033101609",
"https://doi.org/10.1007/bf01238220"
],
"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": "https://doi.org/10.1016/j.laa.2003.11.003",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1037191330"
],
"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": "https://doi.org/10.1016/s0024-3795(02)00734-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1049556885"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/s0024-3795(02)00734-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1049556885"
],
"type": "CreativeWork"
}
],
"datePublished": "2006",
"datePublishedReg": "2006-01-01",
"description": "We define and solve a boundary interpolation problem for generalized Schur functions s(z) on the open unit disk \\( \\mathbb{D}\\) which have preassigned asymptotics when z from \\( \\mathbb{D}\\) tends nontangentially to a boundary point z 1 \u2208 \\( \\mathbb{T}\\). The solutions are characterized via a fractional linear parametrization formula. We also prove that a rational J-unitary 2 \u00d7 2-matrix function whose only pole is at z 1 has a unique minimal factorization into elementary factors and we classify these factors. The parametrization formula is then used in an algorithm for obtaining this factorization. In the proofs we use reproducing kernel space methods.",
"editor": [
{
"familyName": "Alpay",
"givenName": "Daniel",
"type": "Person"
},
{
"familyName": "Gohberg",
"givenName": "Israel",
"type": "Person"
}
],
"genre": "chapter",
"id": "sg:pub.10.1007/3-7643-7547-7_1",
"inLanguage": [
"en"
],
"isAccessibleForFree": true,
"isFundedItemOf": [
{
"id": "sg:grant.4109448",
"type": "MonetaryGrant"
}
],
"isPartOf": {
"isbn": [
"3-7643-7546-9"
],
"name": "Interpolation, Schur Functions and Moment Problems",
"type": "Book"
},
"name": "Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions",
"pagination": "1-29",
"productId": [
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/3-7643-7547-7_1"
]
},
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"0cbe7d85cb730b93086dd465370e2468c1319cef03ef27f2f62edc6cab92fb88"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1002676549"
]
}
],
"publisher": {
"location": "Basel",
"name": "Birkh\u00e4user-Verlag",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/3-7643-7547-7_1",
"https://app.dimensions.ai/details/publication/pub.1002676549"
],
"sdDataset": "chapters",
"sdDatePublished": "2019-04-15T16:14",
"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/v90/0000000001_0000000264/records_8675_00000244.jsonl",
"type": "Chapter",
"url": "http://link.springer.com/10.1007/3-7643-7547-7_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.10.1007/3-7643-7547-7_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.10.1007/3-7643-7547-7_1'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/3-7643-7547-7_1'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/3-7643-7547-7_1'
This table displays all metadata directly associated to this object as RDF triples.
132 TRIPLES
23 PREDICATES
36 URIs
20 LITERALS
8 BLANK NODES