Positive extension and completion problems for a class of structured matrices

A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under certain positivity constraints. The extension problem is reduced to a standard interpolation problem for Schur matrix valued functions.

Saved in:
Bibliographic Details
Published inLinear & multilinear algebra Vol. 48; no. 3; pp. 189 - 235
Main Authors Bolotnikov, V., Rodman, L.
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 01.03.2001
Subjects
Online AccessGet full text
ISSN0308-1087
1563-5139
DOI10.1080/03081080108818669

Cover

Abstract A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under certain positivity constraints. The extension problem is reduced to a standard interpolation problem for Schur matrix valued functions.
AbstractList A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under certain positivity constraints. The extension problem is reduced to a standard interpolation problem for Schur matrix valued functions.
Author Bolotnikov, V.
Rodman, L.
Author_xml – sequence: 1
  givenname: V.
  surname: Bolotnikov
  fullname: Bolotnikov, V.
  organization: Department of Mathematics , The College of William and Mary
– sequence: 2
  givenname: L.
  surname: Rodman
  fullname: Rodman, L.
  email: lxrodman@math.wm.edu
  organization: Department of Mathematics , The College of William and Mary
BookMark eNqFkE1LAzEQhoNUsK3-AG_5A6vJJrubgBcpaoWKHvS8zOYDIrtJSVJt_7271FsRD8N8vDwzzLtAMx-8QeiakhtKBLkljIipGENQUdfyDM1pVbOiokzO0HzSi1FsLtAipU9CCKesmqOXt5Bcdl8Gm302PrngMXiNVRi2vclTu42h682QsA0RA1Y9pISDxSnHncq7aDQeIEenTLpE5xb6ZK5-8xJ9PD68r9bF5vXpeXW_KVQpRS5AU9VZyTtaka4SslHGMK241ZKWytZ1ySWMY84NqRvJbNeVHCwhSjINQrElose9KoaUorHtNroB4qGlpJ1saE_8GJnmyDg_PjLAd4i9bjMc-hBtBK9cOqXavM8jefcvyf4-_APkTXt0
Cites_doi 10.1016/0024-3795(81)90215-9
10.1016/0005-1098(88)90095-7
10.1016/S0024-3795(97)00048-7
10.1007/BF01193458
10.1002/mana.19891440118
10.1016/0005-1098(83)90103-6
10.1007/BF01261203
10.1137/S0895479895296471
10.1016/0022-247X(79)90124-0
10.1109/TASSP.1976.1162795
10.1007/978-94-009-0059-2
10.1007/BF01193460
10.1007/BF01691075
10.1007/BF01194989
10.1137/1037082
10.1080/03081089008817973
10.1017/CBO9780511569678.010
ContentType Journal Article
Copyright Copyright Taylor & Francis Group, LLC 2001
Copyright_xml – notice: Copyright Taylor & Francis Group, LLC 2001
DBID AAYXX
CITATION
DOI 10.1080/03081080108818669
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1563-5139
EndPage 235
ExternalDocumentID 10_1080_03081080108818669
8818669
GroupedDBID -~X
.7F
.QJ
0BK
0R~
1TA
30N
4.4
5GY
5VS
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABUFD
ABXUL
ABXYU
ACAGQ
ACGEJ
ACGFS
ACIWK
ACTIO
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFRVT
AGDLA
AGMYJ
AGROQ
AHDZW
AHMOU
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALCKM
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AMEWO
AQRUH
AQTUD
AVBZW
AWYRJ
BLEHA
CAG
CCCUG
CE4
COF
CRFIH
CS3
DGEBU
DKSSO
DMQIW
DU5
EBS
EJD
E~A
E~B
GTTXZ
H13
HZ~
H~P
J.P
KYCEM
M4Z
NA5
NY~
O9-
P2P
PQQKQ
QCRFL
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TN5
TOXWX
TTHFI
TUROJ
TWF
UPT
UT5
UU3
YQT
ZGOLN
~S~
07G
29L
AAIKQ
AAKBW
AAYXX
ABEFU
ACGEE
ACTCW
ADIYS
AEUMN
AFFNX
AGCQS
AGLEN
AMVHM
AMXXU
BCCOT
BPLKW
C06
CITATION
DWIFK
HF~
IPNFZ
IVXBP
LJTGL
NUSFT
RIG
TAQ
TFMCV
UB9
UU8
V3K
V4Q
ID FETCH-LOGICAL-c298t-ad1cbf94b150b5897cee3dc4fd912cf66249a89744e06793fbb24af00c93da8c3
ISSN 0308-1087
IngestDate Wed Oct 01 02:43:32 EDT 2025
Mon May 13 12:09:03 EDT 2019
Mon Oct 20 23:46:39 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 3
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c298t-ad1cbf94b150b5897cee3dc4fd912cf66249a89744e06793fbb24af00c93da8c3
PageCount 47
ParticipantIDs crossref_primary_10_1080_03081080108818669
informaworld_taylorfrancis_310_1080_03081080108818669
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 3/1/2001
PublicationDateYYYYMMDD 2001-03-01
PublicationDate_xml – month: 03
  year: 2001
  text: 3/1/2001
  day: 01
PublicationDecade 2000
PublicationTitle Linear & multilinear algebra
PublicationYear 2001
Publisher Gordon and Breach Science Publishers
Publisher_xml – name: Gordon and Breach Science Publishers
References Dym H. (CIT0014) 1989; 71
Gohberg I. (CIT0024) 1993; 63
CIT0030
CIT0010
Foias C. (CIT0022) 1998; 100
Bolotnikov (CIT0008) 1990; 45
CIT0031
CIT0033
Heinig G. (CIT0026) 1984; 13
Constantinescu T. (CIT0011) 1996; 82
Alpay D. (CIT0001) 1998; 6
CIT0016
Foias C. (CIT0021) 1990; 44
Gohberg I. (CIT0025) 1989; 22
CIT0015
CIT0018
CIT0017
CIT0019
Alpay D. (CIT0005) 1997; 23
Ball J. A. (CIT0007) 1990; 45
CIT0020
CIT0023
Woerdeman H. J. (CIT0036) 1989
Bakonyi M. (CIT0006) 1992; 261
Rosenblum M. (CIT0034) 1985
CIT0003
CIT0002
Dubovoj V. K. (CIT0012) 1982; 37
CIT0027
Johnson C. R. (CIT0028) 1988; 35
Sakhnovich L. A. (CIT0035) 1997
Dubovoj V.K. (CIT0013) 1992; 129
CIT0029
Marshall A. W. (CIT0032) 1979
Alpay D. (CIT0004) 1997; 23
CIT0009
References_xml – volume-title: Hardy classes and operator theory
  year: 1985
  ident: CIT0034
– ident: CIT0017
  doi: 10.1016/0024-3795(81)90215-9
– volume: 71
  volume-title: CBMS Regional Conference Series in Mathematics
  year: 1989
  ident: CIT0014
– ident: CIT0031
  doi: 10.1016/0005-1098(88)90095-7
– ident: CIT0002
  doi: 10.1016/S0024-3795(97)00048-7
– volume: 45
  volume-title: Operator Theory: Advances and Applications
  year: 1990
  ident: CIT0007
– ident: CIT0003
  doi: 10.1007/BF01193458
– volume: 63
  volume-title: Operator Theory: Advances and Applications
  year: 1993
  ident: CIT0024
– ident: CIT0023
  doi: 10.1002/mana.19891440118
– volume: 35
  start-page: 107
  year: 1988
  ident: CIT0028
  publication-title: Operator Theory: Advances and Applications
– volume: 13
  volume-title: Operator Theory: Advances and Applications
  year: 1984
  ident: CIT0026
– ident: CIT0027
  doi: 10.1016/0005-1098(83)90103-6
– ident: CIT0018
  doi: 10.1007/BF01261203
– volume: 22
  start-page: 109
  year: 1989
  ident: CIT0025
  publication-title: Journal of Operator Theory
– ident: CIT0010
  doi: 10.1137/S0895479895296471
– ident: CIT0029
  doi: 10.1016/0022-247X(79)90124-0
– ident: CIT0033
  doi: 10.1109/TASSP.1976.1162795
– volume-title: Interpolation theory and its applications
  year: 1997
  ident: CIT0035
  doi: 10.1007/978-94-009-0059-2
– volume: 261
  volume-title: Pitman Research Notes in Mathematics Series
  year: 1992
  ident: CIT0006
– volume: 129
  volume-title: Teubner Texts in Mathematics
  year: 1992
  ident: CIT0013
– volume-title: CWI Tract
  year: 1989
  ident: CIT0036
– volume: 82
  volume-title: Operator Theory: Advances and Applications
  year: 1996
  ident: CIT0011
– ident: CIT0015
  doi: 10.1007/BF01193460
– volume: 6
  volume-title: Panoramas et Synthéses
  year: 1998
  ident: CIT0001
– ident: CIT0016
  doi: 10.1007/BF01691075
– ident: CIT0009
  doi: 10.1007/BF01194989
– volume: 44
  volume-title: Operator Theory: Advances and Applications
  year: 1990
  ident: CIT0021
– volume: 23
  year: 1997
  ident: CIT0005
  publication-title: Operator Theory: Advances and Applications
– ident: CIT0030
  doi: 10.1137/1037082
– volume: 23
  start-page: 539
  year: 1997
  ident: CIT0004
  publication-title: Houston Journal of Mathematics
– volume: 45
  year: 1990
  ident: CIT0008
  publication-title: Operator Theory: Advances and Applications
– ident: CIT0019
  doi: 10.1080/03081089008817973
– volume: 37
  start-page: 14
  year: 1982
  ident: CIT0012
  publication-title: Teoriya Funktsii, Funktsional'nyl Analiz i ikh Prilozheniya
– ident: CIT0020
  doi: 10.1017/CBO9780511569678.010
– volume: 100
  volume-title: Operator Theory: Advances and Applications
  year: 1998
  ident: CIT0022
– volume-title: Inequalities: Theory of majorization and its applications
  year: 1979
  ident: CIT0032
SSID ssj0004135
Score 1.5122982
Snippet A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under...
SourceID crossref
informaworld
SourceType Index Database
Enrichment Source
Publisher
StartPage 189
SubjectTerms AMS Subject Classification: 15A45, 15A48
Generalized Toeplitz
Positive completions
Positive extensions
Schur interpolation problem
Structured matrices
Title Positive extension and completion problems for a class of structured matrices
URI https://www.tandfonline.com/doi/abs/10.1080/03081080108818669
Volume 48
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVLSH
  databaseName: aylor and Francis Online
  customDbUrl:
  mediaType: online
  eissn: 1563-5139
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0004135
  issn: 0308-1087
  databaseCode: AHDZW
  dateStart: 19970101
  isFulltext: true
  providerName: Library Specific Holdings
– providerCode: PRVAWR
  databaseName: Taylor & Francis Science and Technology Library-DRAA
  customDbUrl:
  eissn: 1563-5139
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0004135
  issn: 0308-1087
  databaseCode: 30N
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: http://www.tandfonline.com/page/title-lists
  providerName: Taylor & Francis
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9tAEF614UIPCEpRQynaQ08gR_bu2rGPQB9RpVQ9BIF6ifYpobYJIgYhfn1nX7YDFEEOsZxN7LVmxrOzu998g9AnUxhjlGaJlqlKGOMmqYhQSTakmjGiyLC0ucPjH8XolH0_z887Gdc2u6QWA3n3aF7JKlqFNtCrzZJ9gWabm0IDnIN-4QgahuOzdPzTIa5u9KFbyl5EZLGDiWun2FAvZuHBkofSxso2PvS0sdcWfP7XkfQHKGHMjIbYk_vKGw5x-Md_tzVBxFU7hQfHWc8ufs9vHFp20G7eqJjSMFhaVejAqpwdfIOZb3jm4ysL62xcTYvW73gq6jhiw8ipgyctaJJnnqkoulpWdkyKdvxm5usIhSGYeAaTB949wCGhN3sKH0fXV7VDWQMwDL-8RmsEvH3aQ2tHo8-_ztqM2VB6NT543O-2rOv3b78UsSzx2XYikckm2ghTCHzk7WELvdKzt-jNuOHfXWyjcbQM3FgGBinj1jJwtAwMHWGOnWXgucGtZeBoGe_Q6dcvk5NREgpnJJJUZZ1wlUlhKiYg2hd5WQ0hEqJKMqOqjEhTFDDn5tDMmLbriNQIQeAtTVNZUcVLSXdQbzaf6fcIa23Skgtl99tZrjNeUcmFTjlJNctF3kcHUTjTS8-PMs0i7ex9SfZR2hXftHaLUsZXkHn492l9W_dR_sQl9L9d7a543Qe03r4Oe6gHMtcfIeysxX6woX96T4JD
linkProvider Library Specific Holdings
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV05T8MwFH6CMgADN6KcHpiQUpLYuUaEqAo0FUMrdYt8LogWkRQhfj22k9CDY-gQKYriOH7PiZ8_f_4ewKUKlVJCEkdyVziEUOUkPhOOF2FJiC_8KDZ7h9Ne2BmQh2EwrAC3vKJVmjm0KoUi7L_afNwGjK4pcddGY8Wc6MMKtiWrsBboQN9kMMBub7ovskqwia2EaRzVq5q_PWJuXJpTLZ0Zb9rbkNVvWtJMnluTgrX454KI4_JN2YGtKhRFN2Xf2YUVOdqDzfRbxzXfh_TJcrreJbJguUHWkK4LWSK6ND5FVUaaHOmmIIq4icbRWKFSmHbyJgV6sWkAZH4Ag_Zd_7bjVAkYHO4nceFQ4XGmEsJ01MiCOIn0iIoFJ0okns9VGOq5G9WXCZEGj8KKMV9723V5ggWNOT6Exmg8kkeApFRuTJkw67YkkB5NMKdMutR3JQlY0ISr2vzZa6mzkXm1fOmijZrgzjooKyy4ocpMJD9vz4qPognBP0Xwn1UdL1nuAtY7_bSbde97jyewMWWunUJD21-e6VCmYOe2v34BkizqXw
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwELagSAgG3ojy9MCElJLEThqPCKjKo1UHKnWL_DgviLYiKUL8emwngbY8hg6RosiO5Tsnd777_B1C5zrWWiugHkhfeZRy7bFQKC9oEqA0VGEzsWeHO9243af3g2hQYnOyElZp99C6IIpw_2r7cY-VrhBxl5Zixd6Yy_G1sWW0EtuMmD3B4Xe_j0WW9TWJYzBNmlVS87dXzJilGdLSKXPT2ixqqmaOpdCiTJ4bk1w05Mcch-PCM9lCG6Ujiq-KlbONlmC4g9Y7Xyyu2S7q9Byi6w2wC5XbuBo2Q2EHQwerUVzWo8mwmQnmWFpfHI80LmhpJ6-g8IsrAgDZHuq3bp-u215ZfsGTIUtyj6tACs2oMD6jiBLWNPaUKEm1YkEodRybnRs3jykFG40iWojQ6Nr3JSOKJ5Lso9pwNIQDhAG0n3ChbNaWRhBwRiQX4PPQBxqJqI4uKumn44JlIw0q8tJ5GdWRP62fNHehDV3UIfnZPM3f8zqK_ulC_hzqcMF-Z2i1d9NKH--6D0do7Ru2doxqRvxwYvyYXJy61foJwlnpAw
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Positive+extension+and+completion+problems+for+a+class+of+structured+matrices&rft.jtitle=Linear+%26+multilinear+algebra&rft.au=Bolotnikov%2C+V.&rft.au=Rodman%2C+L.&rft.date=2001-03-01&rft.pub=Gordon+and+Breach+Science+Publishers&rft.issn=0308-1087&rft.eissn=1563-5139&rft.volume=48&rft.issue=3&rft.spage=189&rft.epage=235&rft_id=info:doi/10.1080%2F03081080108818669&rft.externalDocID=8818669
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0308-1087&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0308-1087&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0308-1087&client=summon