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Orthogonal Matrix-valued Polynomials and Applications

Seminar on Operator Theory at the School of Mathematical Sciences, Tel Aviv University

  • I. Gohberg

Part of the Operator Theory: Advances and Applications book series (OT, volume 34)

About this book

Introduction

This paper is a largely expository account of the theory of p x p matrix polyno­ mials associated with Hermitian block Toeplitz matrices and some related problems of interpolation and extension. Perhaps the main novelty is the use of reproducing kernel Pontryagin spaces to develop parts of the theory in what hopefully the reader will regard as a reasonably lucid way. The topics under discussion are presented in a series of short sections, the headings of which give a pretty good idea of the overall contents of the paper. The theory is a rich one and the present paper in spite of its length is far from complete. The author hopes to fill in some of the gaps in future publications. The story begins with a given sequence h_n" ... , hn of p x p matrices with h-i = hj for j = 0, ... , n. We let k = O, ... ,n, (1.1) denote the Hermitian block Toeplitz matrix based on ho, ... , hk and shall denote its 1 inverse H k by (k)] k [ r = .. k = O, ... ,n, (1.2) k II} . '-0 ' I- whenever Hk is invertible.

Keywords

boundary element method Finite Interpolation kernel Mathematica matrices Matrix operator operator theory orthogonal polynomials polynomial story theorem university

Editors and affiliations

  • I. Gohberg
    • 1
  1. 1.School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-5472-6
  • Copyright Information Birkhäuser Basel 1988
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-5474-0
  • Online ISBN 978-3-0348-5472-6
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site
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