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Field name	Details
Dewey Class	500
Title	New Aspects in Interpolation and Completion Theories ([EBook]) / edited by I. Gohberg.
Added Personal Name	Gohberg, Israel , 1928-2009
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 1993.
Physical Details	X, 221 pages : online resource.
Series	Operator theory : advances and applications ; 64
ISBN	9783034885621
Summary Note	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.:
Contents note	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. Some formulas for DB? -- 3. The role of DA?2II0* -- 4. The four block problem -- 5. Optimal solutions -- 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-8562-1
Links to Related Works	Subject References: Interpolation spaces . Science . Science, general . Authors: editor . Gohberg, Israel 1928-2009 . Corporate Authors: SpringerLink (Online service) . Series: Operator theory : advances and applications . Classification: 500 .

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New Aspects in Interpolation and Completion Theories

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