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New Aspects in Interpolation and Completion Theories

  • I. Gohberg

Part of the Operator Theory Advances and Applications book series (OT, volume 64)

Table of contents

  1. Front Matter
    Pages I-X
  2. Mihály Bakonyi, Victor G. Kaftal, Gary Weiss, Hugo J. Woerdeman
    Pages 23-32
  3. Joseph A. Ball, Israel Gohberg, Leiba Rodman
    Pages 73-102
  4. Hong-Ke Du, Caixing Gu
    Pages 103-117
  5. C. Foias, A. E. Frazho, W. S. Li
    Pages 119-156
  6. A. E. Frazho, S. M. Kherat
    Pages 157-202
  7. Israel Gohberg, Caixing Gu
    Pages 203-217
  8. Back Matter
    Pages 218-221

About this book

Introduction

This volume consists of eight papers containing recent advances in interpolation theory for matrix functions and completion theory for matrices and operators. In the first paper, D. Alpay and P. Loubaton, "The tangential trigonometric moment problem on an interval and related topics" a trigonometric moment problem on an interval for matrix valued functions is studied. The realization approach plays an important role in solving this problem. The second paper, M. Bakonyi, V.G. Kaftal, G. Weiss and H.J. Woerdeman, "Max­ imum entropy and joint norm bounds for operator extensions" is dedicated to a matrix completion problem. In it is considered the problem when only the lower triangular part of the operator entries of a matrix is identified. Completions which have simultaneously a small usual norm and a small Hilbert-Schmidt norm are considered. Bounds for these norms are obtained. The analysis of the maximum entropy extension plays a special role. The paper contains applications to nest algebras and integral operators. The third paper, J .A. Ball, I. Gohberg and M.A. Kaashoek, "Bitangential interpola­ tion for input-output operators of time varying systems: the discrete time case" contains solutions of time varying interpolation problems. The main attention is focused on the time varying analog of the Nevanlinna-Pick tangential problem in the case where the inter­ polation conditions appear from two sides. The state space theory of time varying systems play an important role.

Keywords

Interpolation Operator theory differential equation linear optimization maximum

Editors and affiliations

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

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