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Orthogonal Systems and Convolution Operators

  • Robert L. Ellis
  • Israel Gohberg

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Robert L. Ellis, Israel Gohberg
    Pages 1-27
  3. Robert L. Ellis, Israel Gohberg
    Pages 29-36
  4. Robert L. Ellis, Israel Gohberg
    Pages 53-70
  5. Robert L. Ellis, Israel Gohberg
    Pages 71-86
  6. Robert L. Ellis, Israel Gohberg
    Pages 87-98
  7. Robert L. Ellis, Israel Gohberg
    Pages 99-114
  8. Robert L. Ellis, Israel Gohberg
    Pages 115-142
  9. Robert L. Ellis, Israel Gohberg
    Pages 143-161
  10. Robert L. Ellis, Israel Gohberg
    Pages 163-182
  11. Robert L. Ellis, Israel Gohberg
    Pages 183-203
  12. Robert L. Ellis, Israel Gohberg
    Pages 205-226
  13. Back Matter
    Pages 227-236

About this book

Introduction

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.

Keywords

C*-algebra Operator theory convolution distribution orthogonal polynomials

Authors and affiliations

  • Robert L. Ellis
    • 1
  • Israel Gohberg
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityIL - Ramat AvivIsrael

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