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New Aspects in Interpolation and Completion Theories

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 tri...

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Bibliographic Details
Other Authors: Gohberg, I. (Editor)
Format: eBook
Language:English
Published: Basel Birkhäuser 1993, 1993
Edition:1st ed. 1993
Series:Operator Theory: Advances and Applications
Subjects:
Humanities And Social Sciences
Humanities
Social Sciences
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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
  • 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
  • Maximum entropy and joint norm bounds for operator extensions
  • 1. Introduction
  • 2. A sharp bound in the 2×2 case
  • 3. The maximum entropy method
  • 4. An application to integral operators
  • References
  • 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
  • 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
  • On the spectra of operator completion problems
  • 1. Introduction
  • 2. Case of finite dimensional spaces
  • 3. Case of infinite dimensional spaces
  • References
  • The exact H2 estimate for the central H? interpolant
  • 1. An improved Kaftal-Larson-Weiss estimate
  • 2. Someformulas for DB?
  • 3. The role of DA?2II0*
  • 4. The four block problem
  • 5. Optimal solutions
  • References

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