Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2006

AUTHORS

Daniel Alpay , Aad Dijksma , Heinz Langer , Gerald Wanjala

ABSTRACT

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 ∈ \( \mathbb{T}\). 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... »

PAGES

1-29

Book

TITLE

Interpolation, Schur Functions and Moment Problems

ISBN

3-7643-7546-9

From Grant

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/3-7643-7547-7_1

DOI

http://dx.doi.org/10.1007/3-7643-7547-7_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1002676549


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, 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

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.10.1007/3-7643-7547-7_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

Subject Predicate Object
1 sg:pub.10.1007/3-7643-7547-7_1 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N6480c7b8ffe74035893a0f0d12ce8e47
4 schema:citation sg:pub.10.1007/bf01200325
5 sg:pub.10.1007/bf01204261
6 sg:pub.10.1007/bf01238220
7 sg:pub.10.1007/bf01691925
8 https://doi.org/10.1016/0022-1236(78)90064-2
9 https://doi.org/10.1016/0022-247x(75)90093-1
10 https://doi.org/10.1016/j.laa.2003.11.003
11 https://doi.org/10.1016/j.laa.2004.02.037
12 https://doi.org/10.1016/s0024-3795(02)00734-6
13 schema:datePublished 2006
14 schema:datePublishedReg 2006-01-01
15 schema: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 ∈ \( \mathbb{T}\). 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.
16 schema:editor N3982a917781d4c86bbf419d691f42705
17 schema:genre chapter
18 schema:inLanguage en
19 schema:isAccessibleForFree true
20 schema:isPartOf Ne3a580f26d7e426d9e3ff442d2661634
21 schema:name Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions
22 schema:pagination 1-29
23 schema:productId N0a674ad89d484762ac4bba21d0c42d05
24 N5cde1cf665494f2995e7f3d39a615c0b
25 N71670bf803db47afbff5b8076d6e9ab7
26 schema:publisher N6a84323211214b8695b68bd6cc1a8df8
27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002676549
28 https://doi.org/10.1007/3-7643-7547-7_1
29 schema:sdDatePublished 2019-04-15T16:14
30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
31 schema:sdPublisher N1e1a453b11354a6ba3e977aaeb68bb61
32 schema:url http://link.springer.com/10.1007/3-7643-7547-7_1
33 sgo:license sg:explorer/license/
34 sgo:sdDataset chapters
35 rdf:type schema:Chapter
36 N01f00122e5fe4eb7b5d09b33f0cb4953 rdf:first sg:person.013762723211.39
37 rdf:rest N76ade184cdb644c7aa0d6feb3c550983
38 N0a674ad89d484762ac4bba21d0c42d05 schema:name readcube_id
39 schema:value 0cbe7d85cb730b93086dd465370e2468c1319cef03ef27f2f62edc6cab92fb88
40 rdf:type schema:PropertyValue
41 N1e1a453b11354a6ba3e977aaeb68bb61 schema:name Springer Nature - SN SciGraph project
42 rdf:type schema:Organization
43 N3982a917781d4c86bbf419d691f42705 rdf:first Nd931b2713c65484ca88724b0995c3e48
44 rdf:rest N3e29bbe2c9894f4fb47293f824009998
45 N3e29bbe2c9894f4fb47293f824009998 rdf:first N4009ab8c854a4fe39b7409375eabc7be
46 rdf:rest rdf:nil
47 N4009ab8c854a4fe39b7409375eabc7be schema:familyName Gohberg
48 schema:givenName Israel
49 rdf:type schema:Person
50 N534f2283553e40df90fb00e44992bbc1 rdf:first sg:person.012754335703.52
51 rdf:rest rdf:nil
52 N5cde1cf665494f2995e7f3d39a615c0b schema:name doi
53 schema:value 10.1007/3-7643-7547-7_1
54 rdf:type schema:PropertyValue
55 N6480c7b8ffe74035893a0f0d12ce8e47 rdf:first sg:person.011517101346.40
56 rdf:rest N01f00122e5fe4eb7b5d09b33f0cb4953
57 N6a84323211214b8695b68bd6cc1a8df8 schema:location Basel
58 schema:name Birkhäuser-Verlag
59 rdf:type schema:Organisation
60 N71670bf803db47afbff5b8076d6e9ab7 schema:name dimensions_id
61 schema:value pub.1002676549
62 rdf:type schema:PropertyValue
63 N76ade184cdb644c7aa0d6feb3c550983 rdf:first sg:person.07450173411.71
64 rdf:rest N534f2283553e40df90fb00e44992bbc1
65 Nd931b2713c65484ca88724b0995c3e48 schema:familyName Alpay
66 schema:givenName Daniel
67 rdf:type schema:Person
68 Ne3a580f26d7e426d9e3ff442d2661634 schema:isbn 3-7643-7546-9
69 schema:name Interpolation, Schur Functions and Moment Problems
70 rdf:type schema:Book
71 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
72 schema:name Mathematical Sciences
73 rdf:type schema:DefinedTerm
74 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
75 schema:name Pure Mathematics
76 rdf:type schema:DefinedTerm
77 sg:grant.4109448 http://pending.schema.org/fundedItem sg:pub.10.1007/3-7643-7547-7_1
78 rdf:type schema:MonetaryGrant
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.012754335703.52 schema:affiliation https://www.grid.ac/institutes/grid.33440.30
85 schema:familyName Wanjala
86 schema:givenName Gerald
87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012754335703.52
88 rdf:type schema:Person
89 sg:person.013762723211.39 schema:affiliation https://www.grid.ac/institutes/grid.4830.f
90 schema:familyName Dijksma
91 schema:givenName Aad
92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013762723211.39
93 rdf:type schema:Person
94 sg:person.07450173411.71 schema:affiliation https://www.grid.ac/institutes/grid.5329.d
95 schema:familyName Langer
96 schema:givenName Heinz
97 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07450173411.71
98 rdf:type schema:Person
99 sg:pub.10.1007/bf01200325 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039094925
100 https://doi.org/10.1007/bf01200325
101 rdf:type schema:CreativeWork
102 sg:pub.10.1007/bf01204261 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001047275
103 https://doi.org/10.1007/bf01204261
104 rdf:type schema:CreativeWork
105 sg:pub.10.1007/bf01238220 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033101609
106 https://doi.org/10.1007/bf01238220
107 rdf:type schema:CreativeWork
108 sg:pub.10.1007/bf01691925 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019968975
109 https://doi.org/10.1007/bf01691925
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1016/0022-1236(78)90064-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035417758
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1016/0022-247x(75)90093-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011894065
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1016/j.laa.2003.11.003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037191330
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1016/j.laa.2004.02.037 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031956638
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1016/s0024-3795(02)00734-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049556885
120 rdf:type schema:CreativeWork
121 https://www.grid.ac/institutes/grid.33440.30 schema:alternateName Mbarara University of Science and Technology
122 schema:name Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410, Mbarara, Uganda
123 rdf:type schema:Organization
124 https://www.grid.ac/institutes/grid.4830.f schema:alternateName University of Groningen
125 schema:name Department of Mathematics, University of Groningen, P.O. Box 800, NL-9700 AV Groningen, The Netherlands
126 rdf:type schema:Organization
127 https://www.grid.ac/institutes/grid.5329.d schema:alternateName TU Wien
128 schema:name Institute of Analysis and Computational Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
129 rdf:type schema:Organization
130 https://www.grid.ac/institutes/grid.7489.2 schema:alternateName Ben-Gurion University of the Negev
131 schema:name Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel
132 rdf:type schema:Organization
 




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


...