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Erschienen in:
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2023 | OriginalPaper | Buchkapitel

8. Block Jacobi Type Matrices and the Two Dimensional Real Moment Problem

verfasst von : Yurij M. Berezansky, Mykola E. Dudkin

Erschienen in: Jacobi Matrices and the Moment Problem

Verlag: Springer Nature Switzerland

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Abstract

The chapter proposes an analogue of Jacobi type bock matrices, which are related to the real power two-dimensional moment problem and the corresponding polynomials orthogonal with respect to some probability measure on the real plane. In this case, two commutative block matrices are also obtained, which have a tri-diagonal block structure and are self-adjoint operators in the \(l_2\) space like the space of square summable sequences. The existence of a one-to-one correspondence between the probability measure on the compact set of the real plane and such matrices is also proved.

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Vorheriges Kapitel Block Jacobi Type Matrices and the Complex Moment Problem in the Exponential Form
Nächstes Kapitel Applications of the Spectral Theory of Jacobi Matrices and Their Generalizations to the Integration of Nonlinear Equations
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Metadaten
Titel
Block Jacobi Type Matrices and the Two Dimensional Real Moment Problem
verfasst von
Yurij M. Berezansky
Mykola E. Dudkin
Copyright-Jahr
2023
Buch
Jacobi Matrices and the Moment Problem

Print ISBN: 978-3-031-46386-0

Electronic ISBN: 978-3-031-46387-7

Copyright-Jahr: 2023

DOI
https://doi.org/10.1007/978-3-031-46387-7_8

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