New Aspects in Interpolation and Completion Theories

1. Front Matter

   Pages I-X

   PDF

2. The tangential trigonometric moment problem on an interval and related topics

   • Daniel Alpay, Philippe Loubaton

   Pages 1-21

3. Maximum Entropy and Joint Norm Bounds for Operator Extensions

   • Mihály Bakonyi, Victor G. Kaftal, Gary Weiss, Hugo J. Woerdeman

   Pages 23-32

4. Bitangential Interpolation for Input-Out Operators of Time-Varying Systems: The Discrete Time Case

   • J. A. Ball, I. Gohberg, M. A. Kaashoek

   Pages 33-72

5. Two-Sided Tangential Interpolation of Real Rational Matrix Functions

   • Joseph A. Ball, Israel Gohberg, Leiba Rodman

   Pages 73-102

6. On The Spectra of Operator Completion Problems

   • Hong-Ke Du, Caixing Gu

   Pages 103-117

7. The Exact H2 Estimate for the Central H∞ Interpolant

   • C. Foias, A. E. Frazho, W. S. Li

   Pages 119-156

8. On Mixed H2 - H∞ Tangential Interpolation

   • A. E. Frazho, S. M. Kherat

   Pages 157-202

9. On a Completion Problem for Matrices

   • Israel Gohberg, Caixing Gu

   Pages 203-217

10. Back Matter

    Pages 218-221

    PDF

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.

• Interpolation
• Operator theory
• differential equation
• linear optimization
• maximum

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

  I. Gohberg

Policies and ethics