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Orthogonal Systems and Convolution Operators

  • Book
  • © 2003

Overview

Authors:
  1. Robert L. Ellis

    1. Department of Mathematics, University of Maryland, College Park, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Israel Gohberg

    1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, IL - Ramat Aviv, Israel

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 140)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Orthogonal Polynomials and Krein’s Theorem

    • Robert L. Ellis, Israel Gohberg
    Pages 1-27

  3. Reformulations of Krein’s Theorem

    • Robert L. Ellis, Israel Gohberg
    Pages 29-36

  4. Inner Products on Modules and Orthogonalization with Invertible Squares

    • Robert L. Ellis, Israel Gohberg
    Pages 37-51

  5. Orthogonal Matrix Polynomials

    • Robert L. Ellis, Israel Gohberg
    Pages 53-70

  6. Special Class of Block Toeplitz Matrices

    • Robert L. Ellis, Israel Gohberg
    Pages 71-86

  7. Orthogonal Operator-Valued Polynomials: First Generalization

    • Robert L. Ellis, Israel Gohberg
    Pages 87-98

  8. Convolution Equations on a Finite Interval

    • Robert L. Ellis, Israel Gohberg
    Pages 99-114

  9. Continuous Analogues of Orthogonal Matrix Polynomials

    • Robert L. Ellis, Israel Gohberg
    Pages 115-142

  10. Orthogonal Operator-Valued Polynomials

    • Robert L. Ellis, Israel Gohberg
    Pages 143-161

  11. Reverse, Left and Right Orthogonalization

    • Robert L. Ellis, Israel Gohberg
    Pages 163-182

  12. Discrete Infinite Analogue of Krein’s Theorem

    • Robert L. Ellis, Israel Gohberg
    Pages 183-203

  13. Continuous Infinite Analogue of Krein’s Theorem

    • Robert L. Ellis, Israel Gohberg
    Pages 205-226

  14. Back Matter

    Pages 227-236
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Keywords

About this book

In this book we study orthogonal polynomials and their generalizations in spaces with weighted inner products. The impetus for our research was a deep theorem due to M.G. Krein along with subsequent results of Krein and H. Langer. Together with our colleagues, we have worked in this area for nearly fifteen years, and the results of our research are presented here in unified form. We are grateful to the Department of mathematics at the University of Maryland in College Park and to Tel-Aviv University for their support and encouragement. The support of the Silver Family Foundation is also highly appreciated. Introduction The starting point ofthis book is a study ofthe orthogonal polynomials {qn In ?: O} obtained by orthogonalizing the power functions I, Z, z2, ... on the unit circle. The orthogonality is with respect to the scalar product defined by where the weight w is a positive integrable function on the unit circle. These ortho­ gonal polynomials are called the Szego polynomials associated with the weight w.

Authors and Affiliations

  • Department of Mathematics, University of Maryland, College Park, USA

    Robert L. Ellis

  • School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, IL - Ramat Aviv, Israel

    Israel Gohberg

Bibliographic Information

  • Book Title: Orthogonal Systems and Convolution Operators

  • Authors: Robert L. Ellis, Israel Gohberg

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8045-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2003

  • Hardcover ISBN: 978-3-7643-6929-3Published: 21 November 2002

  • Softcover ISBN: 978-3-0348-9418-0Published: 24 October 2012

  • eBook ISBN: 978-3-0348-8045-9Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XVI, 238

  • Topics: Analysis

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