New Aspects in Interpolation and Completion Theories

This volume consists of eight papers on new advances in interpolation theory for matrix functions and completion theory for matrices and operators. Much emphasis is placed on different interpolation and completion problems when the interpolant is estimated in two different norms. The book also focus...

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Bibliographic Details
Main Author: Gohberg, I.
Format: eBook
Language:English
Published: Basel Birkhäuser Basel 1993, 1993
Series:Operator Theory Advances and Applications
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a New Aspects in Interpolation and Completion Theories  |h Elektronische Ressource  |c edited by I. Gohberg 
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300 |a X, 221 p  |b online resource 
505 0 |a References -- 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 
505 0 |a 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. Some formulas for DB? -- 3. The role of DA?2II0* -- 4. The four block problem -- 5. Optimal solutions --  
505 0 |a 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) --  
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520 |a This volume consists of eight papers on new advances in interpolation theory for matrix functions and completion theory for matrices and operators. Much emphasis is placed on different interpolation and completion problems when the interpolant is estimated in two different norms. The book also focusses on the study of the spectra of different completions of 2 x 2 block matrices when originally all entries are specified except the lower left corner. A third theme concerns two-sided tangential interpolation problems for real rational matrix functions, and also for the time varying case. A tangential moment problem is also analyzed. All papers deal with related problems of modern matrix analysis, operator theory, complex analysis and system theory and will appeal to a wide group of mathematicians and engineers. The material can be used for advance courses and seminars. Contents: Editorial Introduction ? D. Alpay/P. Loubaton: The tangential trigonometric moment problem on an interval and related topics ? M. Bakonyi/V.G. Kaftal/G. Weiss/H.J. Woerdeman: Maximum entropy and joint norm bounds for operator extensions ? J.A. Ball/I. Gohberg/M.A. Kaashoek: Bitangential interpolation for input-output operators of time varying systems: the discrete time case ? J.A. Ball/I. Gohberg/L. Rodman: Two-sided tangential interpolation of real rational matrix functions ? H. Du/C. Gu: On the spectra of operator completion problems ? C. Foias/A.E. Frazho/W.S. Li: The exact H2 estimate for the central H interpolant ? A.E. Frazho/s.M. Kherat: On mixed H2 - H tangential interpolation ? I. Gohberg/C.Gu: On a completion problem for matrices