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Interpolation, Schur Functions and Moment Problems Book

Interpolation, Schur Functions and Moment Problems
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Interpolation, Schur Functions and Moment Problems, Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal proc, Interpolation, Schur Functions and Moment Problems
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  • Interpolation, Schur Functions and Moment Problems
  • Written by author Daniel Alpay
  • Published by Springer-Verlag New York, LLC, 9/28/2008
  • Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal proc
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Editorial Introduction     ix
Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions   D. Alpay   A. Dijksma   H. Langer   G. Wanjala
Introduction     1
Auxiliary statements     6
The basic interpolation problem at one boundary point     11
Multipoint boundary interpolation     17
J-unitary factorization     20
A factorization algorithm     23
References     27
Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse problems   D. Alpay   I. Gohberg
Introduction     31
Preliminaries     34
The characteristic spectral functions     34
Unitary solutions of the Nehari problem     40
Uniqueness theorem     41
Inverse scattering problem     44
Inverse scattering problem associated to the spectral factor     44
Inverse scattering problem associated to a Blaschke product     46
Other inverse problems     47
Inverse problem associated to the reflection coefficient function     48
Inverse problem associated to the Weyl coefficient function     50
Inverse spectral problem     51
Inverse problem associated to the asymptotic equivalence matrix function     53
The case of two-sided first-order systems     54
A numerical example     56
An example of a non-strictly pseudo-exponential sequence     58
Jacobi matrices     59
References     63
Boundary Nevanlinna-Pick Interpolation Problems for Generalized Schur Functions   V. Bolotnikov   A. Kheifets
Introduction     67
Main results     72
Some preliminaries     77
Fundamental Matrix Inequality     84
Parameters and interpolation conditions     90
Negative squares of the function w = T[subscript curly or open theta epsilon]     104
The degenerate case     109
An example     115
References     118
A Truncated Matricial Moment Problem on a Finite Interval   A. Choque Rivero   Y. Dyukarev   B. Fritzsche   B. Kirstein
Introduction and preliminaries     121
The moment problem     123
Main algebraic identities     128
From the moment problem to the system of fundamental matrix inequalities of Potapov-type     129
From the system of fundamental matrix inequalities to the moment problem      136
Nonnegative column pairs     143
Description of the solution set in the positive definite case     147
A necessary and sufficient condition for the existence of a solution of the moment problem     160
Appendix: Certain subclasses of holomorphic matrix-valued functions and a generalization of Stieltjes' inversion formula     161
Acknowledgement     170
References     170
Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions   V.K. Dubovoy
Introduction     175
Shifts contained in contractions, unitary colligations and characteristic operator functions     178
Shifts contained in contractions and unitary colligations     178
Characteristic operator functions     182
Naimark dilations     182
Construction of a model of a unitary colligation via the Schur parameters of its c.o.f. in the scalar case     185
Schur algorithm, Schur parameters     185
General form of the model     186
Schur determinants and contractive operators. Computation of t[subscript n+1,n]     189
Schur determinants and contractive operators again. Computation of g[subscript n]     192
Description of the model of a unitary colligation if [characters not reproducible] converges      198
Description of the model of a unitary colligation in the case of divergence of the series [characters not reproducible]     202
Description of the model in the case that the function [theta] is a finite Blaschke product     203
Comments     204
A model representation of the maximal shift V[subscript T] contained in a contraction T     207
The conjugate canonical basis     207
A model representation of the maximal unilateral shift V[subscript T] contained in a contraction T     208
The connection of the maximal shifts V[subscript T] and V[subscript T*] with the pseudocontinuability of the corresponding c.o.f. [theta]     220
Pseudocontinuability of Schur functions     220
On some connections between the maximal shifts V[subscript T] and V[subscript T*] and the pseudocontinuability of the corresponding c.o.f. [theta]     222
Some criteria for the pseudocontinuability of a Schur function in terms of its Schur parameters     225
Construction of a countable closed vector system in [characters not reproducible] and investigation of the properties of the sequence [characters not reproducible] of Gram determinants of this system     225
Some criteria of pseudocontinuability of Schur functions     234
On some properties of the Schur parameter sequences of pseudocontinuable Schur functions     238
The structure of pure [Pi]-sequences of rank 0 or 1     244
Acknowledgement     248
References     248
The Matricial Caratheodory Problem in Both Nondegenerate and Degenerate Cases   B. Fritzsche   B. Kirstein   A. Lasarow
Introduction     251
Preliminaries     253
On particular matrix polynomials     257
Description of the set [characters not reproducible]     263
Resolvent matrices which are constructed recursively     272
The nondegenerate case     279
The case of a unique solution     283
References     288
A Gohberg-Heinig type inversion formula involving Hankel operators   G.J. Groenewald   M.A. Kaashoek
Introduction     291
The indicator     293
The main theorem for kernel functions of stable exponential type     295
Proof of the main theorem (general case)     299
References     301


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Interpolation, Schur Functions and Moment Problems, Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal proc, Interpolation, Schur Functions and Moment Problems

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Interpolation, Schur Functions and Moment Problems, Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal proc, Interpolation, Schur Functions and Moment Problems

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Interpolation, Schur Functions and Moment Problems, Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal proc, Interpolation, Schur Functions and Moment Problems

Interpolation, Schur Functions and Moment Problems

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