Ontology type: schema:Chapter Open Access: True
2009
AUTHORSD. Alpay , A. Dijksma , H. Langer
ABSTRACTA Nevanlinna function is a function which is analytic in the open upper half-plane and has a non-negative imaginary paxt there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disk. Applying the transformation p times we find a Nevanlinna function n p which is a fractional linear transformation of the given function n. The main results concern the effect of this transformation to the realizations of n and n p by which we mean their representations through resolvents of self-adjoint operators in Hilbert space. Our tools are block operator matrix representations, u-resolvent matrices, and reproducing kernel Hilbert spaces. More... »
PAGES27-63
Modern Analysis and Applications
ISBN
978-3-7643-9918-4
978-3-7643-9919-1
http://scigraph.springernature.com/pub.10.1007/978-3-7643-9919-1_4
DOIhttp://dx.doi.org/10.1007/978-3-7643-9919-1_4
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1050943660
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\u00a0Beer-Sheva, Israel"
],
"type": "Organization"
},
"familyName": "Alpay",
"givenName": "D.",
"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 407, 9700\u00a0AK Groningen, The Netherlands"
],
"type": "Organization"
},
"familyName": "Dijksma",
"givenName": "A.",
"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 for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040\u00a0Vienna, Austria"
],
"type": "Organization"
},
"familyName": "Langer",
"givenName": "H.",
"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(90)90128-y",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1021892747"
],
"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/10.1016/j.laa.2004.02.037",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1031956638"
],
"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/10.1006/jath.2000.3518",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1048561537"
],
"type": "CreativeWork"
}
],
"datePublished": "2009",
"datePublishedReg": "2009-01-01",
"description": "A Nevanlinna function is a function which is analytic in the open upper half-plane and has a non-negative imaginary paxt there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at \u221e, that is an analogue of the Schur transformation for contractive analytic functions in the unit disk. Applying the transformation p times we find a Nevanlinna function n p which is a fractional linear transformation of the given function n. The main results concern the effect of this transformation to the realizations of n and n p by which we mean their representations through resolvents of self-adjoint operators in Hilbert space. Our tools are block operator matrix representations, u-resolvent matrices, and reproducing kernel Hilbert spaces.",
"editor": [
{
"familyName": "Adamyan",
"givenName": "Vadim M.",
"type": "Person"
},
{
"familyName": "Gohberg",
"givenName": "Israel",
"type": "Person"
},
{
"familyName": "Kochubei",
"givenName": "Anatoly",
"type": "Person"
},
{
"familyName": "Popov",
"givenName": "Gennadiy",
"type": "Person"
},
{
"familyName": "Berezansky",
"givenName": "Yurij",
"type": "Person"
},
{
"familyName": "Gorbachuk",
"givenName": "Myroslav",
"type": "Person"
},
{
"familyName": "Gorbachuk",
"givenName": "Valentyna",
"type": "Person"
},
{
"familyName": "Langer",
"givenName": "Heinz",
"type": "Person"
}
],
"genre": "chapter",
"id": "sg:pub.10.1007/978-3-7643-9919-1_4",
"inLanguage": [
"en"
],
"isAccessibleForFree": true,
"isPartOf": {
"isbn": [
"978-3-7643-9918-4",
"978-3-7643-9919-1"
],
"name": "Modern Analysis and Applications",
"type": "Book"
},
"name": "The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials",
"pagination": "27-63",
"productId": [
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-3-7643-9919-1_4"
]
},
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"f2ad6f5269fb5635d53217ee794d4b2bd13bfa413ccf3a21523fbe4f2be2ac3d"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1050943660"
]
}
],
"publisher": {
"location": "Basel",
"name": "Birkh\u00e4user Basel",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-3-7643-9919-1_4",
"https://app.dimensions.ai/details/publication/pub.1050943660"
],
"sdDataset": "chapters",
"sdDatePublished": "2019-04-15T13:31",
"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_8664_00000275.jsonl",
"type": "Chapter",
"url": "http://link.springer.com/10.1007/978-3-7643-9919-1_4"
}
]
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.10.1007/978-3-7643-9919-1_4'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-7643-9919-1_4'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-7643-9919-1_4'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-7643-9919-1_4'
This table displays all metadata directly associated to this object as RDF triples.
138 TRIPLES
23 PREDICATES
33 URIs
20 LITERALS
8 BLANK NODES