New Aspects in Interpolation and Completion Theories

Abstract

Editorial Introduction D. Alpay, P. Loubaton The tangential trigonometric moment problem on an interval and related topics 1. Introduction 2. Some lemmas on matrix-valued rational functions 3. The main result 4. The Nevanlinna Pick problem References. M. Bakonyi, V.G. Kaftal, G. Weiss, H.J. Woerdeman Maximum entropy and joint norm bounds for operator extensions 1. Introduction 2. A sharp bound in the 2 x 2 case 3. The maximum entropy method 4. An application to integral operators References. J.A. Ball, 1. Gohberg, M.A. Kaashoek Bitangential interpolation for input-output operators of time varying systems: the discrete time case 0. Introduction 1. Residue calculus and generalized point evaluation 2. Pairs of diagonal operators and homogeneous one-sided interpolation 3. Bitangential interpolation data set 4. Bitangential interpolation in geometric terms 5. Intermezzo about admissible Sylvester data sets 6. Construction of a particular solution 7. Parametrization of all solutions (without norm constraints) 8. Input-output operators of time-varying systems 9. Parametrization of all contractive input-output operators satisfying the bitangential interpolation conditions References. J.A.Ball, I.Gohberg, L. Rodman Two-sided tangential interpolation of real rational matrix functions 1. Introduction 2. Minimal realizations 3. Local data 4. Two-sided tangential interpolation: existence of real interpolants 5. Two-sided tangential interpolation with real-valued data: Description of interpolants 6. Degrees of interpolants 7. Generalized Nevanlinna-Pick interpolation for real rational matrix functions References. H. Du, C. Gu On the spectra of operator completion problems 1. Introduction 2. Case of finite dimensional spaces 3. Case of infinite dimensional spaces References. C. Foias, A.E. Frazho, W.S. Li The exact H2 estimate for the central H interpolant Introduction 1. An improved Kaftal-Larson-Weiss estimate 2. Some formulas for DB 3. The role of DA2II0 4. The four block problem 5. Optimal solutions References. A.E. Frazho, S.M. Kherat On mixed H2 - H tangential interpolation 1. Introduction 2. Formulas for the central solution 3. A state space approach 4. Applications of the H2-H tangential interpolation problem References. I. Gohberg, C. Gu On a completion problem for matrices 1. Introduction 2. Main theorems in the finite dimensional case 3. The full range case 4. The proof of the main theorems in the finite dimensional case 5. Infinite dimensional case References.