New Explicitly Diagonalizable Hankel Matrices Related to the Stieltjes–Carlitz Polynomials
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter k ∈ ( 0 , 1 ) are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space ℓ 2 ( N 0 ) and the solution of the spectral problem is based on an application of the commutator method. Eac...
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| Veröffentlicht in: | Integral equations and operator theory 2021-06, Vol.93 (3), Article 29 |
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| container_title | Integral equations and operator theory |
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| creator | Štampach, František Šťovíček, Pavel |
| description | Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter
k
∈
(
0
,
1
)
are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space
ℓ
2
(
N
0
)
and the solution of the spectral problem is based on an application of the commutator method. Each of the Hankel matrices commutes with a Jacobi matrix which is related to a particular family of the Stieltjes–Carlitz polynomials. More examples of explicitly diagonalizable structured matrix operators are obtained when taking into account also weighted Hankel matrices. |
| doi_str_mv | 10.1007/s00020-021-02638-4 |
| format | Article |
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k
∈
(
0
,
1
)
are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space
ℓ
2
(
N
0
)
and the solution of the spectral problem is based on an application of the commutator method. Each of the Hankel matrices commutes with a Jacobi matrix which is related to a particular family of the Stieltjes–Carlitz polynomials. More examples of explicitly diagonalizable structured matrix operators are obtained when taking into account also weighted Hankel matrices.</description><identifier>ISSN: 0378-620X</identifier><identifier>EISSN: 1420-8989</identifier><identifier>DOI: 10.1007/s00020-021-02638-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Commutators ; Hankel matrices ; Hilbert space ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Polynomials ; Structured matrices</subject><ispartof>Integral equations and operator theory, 2021-06, Vol.93 (3), Article 29</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-964d358f7ffc99ade404ebdc40bc1d7126c746e6cccb53a596260b8fb1be41893</cites><orcidid>0000-0003-3207-6010</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00020-021-02638-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00020-021-02638-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Štampach, František</creatorcontrib><creatorcontrib>Šťovíček, Pavel</creatorcontrib><title>New Explicitly Diagonalizable Hankel Matrices Related to the Stieltjes–Carlitz Polynomials</title><title>Integral equations and operator theory</title><addtitle>Integr. Equ. Oper. Theory</addtitle><description>Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter
k
∈
(
0
,
1
)
are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space
ℓ
2
(
N
0
)
and the solution of the spectral problem is based on an application of the commutator method. Each of the Hankel matrices commutes with a Jacobi matrix which is related to a particular family of the Stieltjes–Carlitz polynomials. More examples of explicitly diagonalizable structured matrix operators are obtained when taking into account also weighted Hankel matrices.</description><subject>Analysis</subject><subject>Commutators</subject><subject>Hankel matrices</subject><subject>Hilbert space</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Polynomials</subject><subject>Structured matrices</subject><issn>0378-620X</issn><issn>1420-8989</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KxDAUhYMoOI6-gKuA62qSpmmzlHF0BP_wB1wIIU1vNWOmHZOIjivfwTf0SYyO4M7F5cDlnAPnQ2ibkl1KSLkXCCGMZITRdCKvMr6CBpSnVyUruYoGJC-rTDByu442QpgmNyuZGKC7M3jB49e5s8ZGt8AHVt_3nXb2TdcO8ER3j-DwqY7eGgj4EpyO0ODY4_gA-CpacHEK4fP9Y6S9s_ENX_Ru0fUzq13YRGttEtj61SG6ORxfjybZyfnR8Wj_JDOsJDGTgjd5UbVl2xopdQOccKgbw0ltaFNSJkzJBQhjTF3kupCCCVJXbU1r4LSS-RDtLHvnvn96hhDVtH_2aUVQrMhZIWWRoAwRW7qM70Pw0Kq5tzPtF4oS9U1RLSmqRFH9UFQ8hfJlKCRzdw_-r_qf1BdDnXcm</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Štampach, František</creator><creator>Šťovíček, Pavel</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-3207-6010</orcidid></search><sort><creationdate>20210601</creationdate><title>New Explicitly Diagonalizable Hankel Matrices Related to the Stieltjes–Carlitz Polynomials</title><author>Štampach, František ; Šťovíček, Pavel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-964d358f7ffc99ade404ebdc40bc1d7126c746e6cccb53a596260b8fb1be41893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Analysis</topic><topic>Commutators</topic><topic>Hankel matrices</topic><topic>Hilbert space</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Polynomials</topic><topic>Structured matrices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Štampach, František</creatorcontrib><creatorcontrib>Šťovíček, Pavel</creatorcontrib><collection>CrossRef</collection><jtitle>Integral equations and operator theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Štampach, František</au><au>Šťovíček, Pavel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New Explicitly Diagonalizable Hankel Matrices Related to the Stieltjes–Carlitz Polynomials</atitle><jtitle>Integral equations and operator theory</jtitle><stitle>Integr. Equ. Oper. Theory</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>93</volume><issue>3</issue><artnum>29</artnum><issn>0378-620X</issn><eissn>1420-8989</eissn><abstract>Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter
k
∈
(
0
,
1
)
are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space
ℓ
2
(
N
0
)
and the solution of the spectral problem is based on an application of the commutator method. Each of the Hankel matrices commutes with a Jacobi matrix which is related to a particular family of the Stieltjes–Carlitz polynomials. More examples of explicitly diagonalizable structured matrix operators are obtained when taking into account also weighted Hankel matrices.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00020-021-02638-4</doi><orcidid>https://orcid.org/0000-0003-3207-6010</orcidid></addata></record> |
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| ispartof | Integral equations and operator theory, 2021-06, Vol.93 (3), Article 29 |
| issn | 0378-620X 1420-8989 |
| language | eng |
| recordid | cdi_proquest_journals_2532599526 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Analysis Commutators Hankel matrices Hilbert space Mathematics Mathematics and Statistics Operators (mathematics) Polynomials Structured matrices |
| title | New Explicitly Diagonalizable Hankel Matrices Related to the Stieltjes–Carlitz Polynomials |
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