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Orthogonal polynomials from Hermitian matrices. II
http://hdl.handle.net/10091/00020587
http://hdl.handle.net/10091/00020587d725aac3-ba84-4666-82d3-719d0cf61252
名前 / ファイル | ライセンス | アクション |
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Item type | 学術雑誌論文 / Journal Article(1) | |||||||||
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公開日 | 2018-05-08 | |||||||||
タイトル | ||||||||||
タイトル | Orthogonal polynomials from Hermitian matrices. II | |||||||||
言語 | ||||||||||
言語 | eng | |||||||||
DOI | ||||||||||
関連識別子 | https://doi.org/10.1063/1.5021462 | |||||||||
関連名称 | 10.1063/1.5021462 | |||||||||
資源タイプ | ||||||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||||||
タイプ | journal article | |||||||||
著者 |
Odake, Satoru
× Odake, Satoru
× Sasaki, Ryu
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信州大学研究者総覧へのリンク | ||||||||||
氏名 | Odake, Satoru | |||||||||
URL | http://soar-rd.shinshu-u.ac.jp/profile/ja.uhLeuUkV.html | |||||||||
出版者 | ||||||||||
出版者 | AMER INST PHYSICS | |||||||||
引用 | ||||||||||
内容記述 | JOURNAL OF MATHEMATICAL PHYSICS. 59(1):013504 (2018) | |||||||||
書誌情報 |
JOURNAL OF MATHEMATICAL PHYSICS 巻 59, 号 1, p. 013504, 発行日 2018-01 |
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抄録 | ||||||||||
内容記述 | This is the second part of the project "unified theory of classical orthogonal polynomials of a discrete variable derived from the eigenvalue problems of Hermitian matrices." In a previous paper, orthogonal polynomials having Jackson integral measures were not included, since such measures cannot be obtained from single infinite dimensional Hermitian matrices. Here we show that Jackson integral measures for the polynomials of the big q-Jacobi family are the consequence of the recovery of self-adjointness of the unbounded Jacobi matrices governing the difference equations of these polynomials. The recovery of self-adjointness is achieved in an extended '2 Hilbert space on which a direct sum of two unbounded Jacobi matrices acts as a Hamiltonian or a difference Schrodinger operator for an infinite dimensional eigenvalue problem. The polynomial appearing in the upper/lower end of the Jackson integral constitutes the eigenvector of each of the two-unbounded Jacobi matrix of the direct sum. We also point out that the orthogonal vectors involving the q-Meixner (q-Charlier) polynomials do not form a complete basis of the '2 Hilbert space, based on the fact that the dual q-Meixner polynomials introduced in a previous paper fail to satisfy the orthogonality relation. The complete set of eigenvectors involving the q-Meixner polynomials is obtained by constructing the duals of the dual q-Meixner polynomials which require the two-component Hamiltonian formulation. An alternative solution method based on the closure relation, the Heisenberg operator solution, is applied to the polynomials of the big q-Jacobi family and their duals and q-Meixner (q-Charlier) polynomials. Published by AIP Publishing. | |||||||||
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内容記述 | Article | |||||||||
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収録物識別子タイプ | ISSN | |||||||||
収録物識別子 | 0022-2488 | |||||||||
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収録物識別子タイプ | NCID | |||||||||
収録物識別子 | AA00701758 | |||||||||
権利 | ||||||||||
権利情報 | © 2018 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. / The following article appeared in JOURNAL OF MATHEMATICAL PHYSICS. 59(1):013504 (2018) and may be found at (https://doi.org/10.1063/1.5021462). | |||||||||
出版タイプ | ||||||||||
出版タイプ | AM | |||||||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||
WoS | ||||||||||
URL | http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=ShinshuUniv&SrcApp=ShinshuUniv&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000424017000042 |