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Jacobi Matrices and the Moment Problem

  • Book
  • © 2023

Overview

Authors:
  1. Yurij M. Berezansky

    1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

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  2. Mykola E. Dudkin

    1. Igor Sikorsky Kyiv Polytechnic Institute, National Technical University of Ukraine, Kyiv, Ukraine

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    You can also search for this author in PubMed   Google Scholar

  • Presents direct and inverse problems for various classes of Jacobi type matrices
  • Uses different approaches and novel methods
  • Develops the theory of block Jacobi matrices and their applications to moment problems

Part of the book series: Operator Theory: Advances and Applications (OT, volume 294)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 1-15

  3. Some Aspects of the Spectral Theory of Unbounded Operators

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 17-119

  4. Jacobi Matrices and the Classical Moment Problem

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 121-181

  5. The Strong Moment Problem

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 183-244

  6. Block Jacobi Type Matrices in the Complex Moment Problem

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 245-287

  7. Unitary Block Jacobi Type Matrices and the Trigonometric Moment Problem

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 289-323

  8. Block Jacobi Type Matrices and the Complex Moment Problem in the Exponential Form

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 325-370

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

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 371-412

  10. Applications of the Spectral Theory of Jacobi Matrices and Their Generalizations to the Integration of Nonlinear Equations

    • Yurij M. Berezansky, Mykola E. Dudkin
    Pages 413-465

  11. Back Matter

    Pages 467-487
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Keywords

About this book

This monograph presents the solution of the classical moment problem, the construction of Jacobi matrices and corresponding polynomials. The cases of strongly,trigonometric, complex and real two-dimensional moment problems are discussed, and the Jacobi-type matrices corresponding to the trigonometric moment problem are shown. The Berezansky theory of the expansion in generalized eigenvectors for corresponding set of commuting operators plays the key role in the proof of results.

The book is recommended for researchers in fields of functional analysis, operator theory, mathematical physics, and engineers who deal with problems of coupled pendulums.

Authors and Affiliations

  • Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Yurij M. Berezansky

  • Igor Sikorsky Kyiv Polytechnic Institute, National Technical University of Ukraine, Kyiv, Ukraine

    Mykola E. Dudkin

Bibliographic Information

  • Book Title: Jacobi Matrices and the Moment Problem

  • Authors: Yurij M. Berezansky, Mykola E. Dudkin

  • Translated by: Mykola E. Dudkin

  • Series Title: Operator Theory: Advances and Applications

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

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-46386-0Published: 30 November 2023

  • Softcover ISBN: 978-3-031-46389-1Due: 31 December 2023

  • eBook ISBN: 978-3-031-46387-7Published: 29 November 2023

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: IX, 487

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Operator Theory, Integral Transforms, Operational Calculus

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