Ebook: Topics in Interpolation Theory

About one half of the papers in this volume are based on lectures which were pre­ sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov. He would have been eighty years old. These have been supplemented by: (1) Historical material, based on reminiscences of former colleagues, students and associates of V.P. Potapov. (2) Translations of a number of important papers (which serve to clarify the Potapov approach to problems of interpolation and extension, as well as a number of related problems and methods) and are relatively unknown in the West. (3) Two expository papers, which have been especially written for this volume. For purposes of discussion, it is convenient to group the technical papers in this volume into six categories. We will now run through them lightly, first listing the major theme, then in parentheses the authors of the relevant papers, followed by discussion. Some supplementary references are listed at the end; OT72 which appears frequently in this volume, refers to Volume 72 in the series Operator Theory: Advances and Applications. It was dedicated to V.P. Potapov. 1. Multiplicative decompositions (Yu.P. Ginzburg; M.S. Livsic, I.V. Mikhailova; V.I. Smirnov).

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This book is devoted primarily to topics in interpolation for scalar, matrix and operator valued functions. About half the papers are based on lectures which were delivered at a conference held at Leipzig University in August 1994 to commemorate the 80th anniversary of the birth of Vladimir Petrovich Potapov. The volume also contains the English translation of several important papers relatively unknown in the West, two expository papers written especially for this volume, and historical material based on reminiscences of former colleagues, students and associates of V.P. Potapov. Numerous examples of interpolation problems of the Nevanlinna-Pick and Carath?odory-Fej?r type are included as well as moment problems and problems of integral representation in assorted settings. The major themes cover applications of the Potapov method of fundamental matrix inequalities, multiplicative decompositions of J-inner matrix valued functions, the abstract interpolation problem, canonical systems of differential equations and interpolation in spaces with an indefinite metric. This book should appeal to a wide range of readers: mathematicians specializing in pure and applied mathematics and engineers who work in systems theory and control. The book will be of use to graduate students and mathematicians interested in functional analysis.

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This book is devoted primarily to topics in interpolation for scalar, matrix and operator valued functions. About half the papers are based on lectures which were delivered at a conference held at Leipzig University in August 1994 to commemorate the 80th anniversary of the birth of Vladimir Petrovich Potapov. The volume also contains the English translation of several important papers relatively unknown in the West, two expository papers written especially for this volume, and historical material based on reminiscences of former colleagues, students and associates of V.P. Potapov. Numerous examples of interpolation problems of the Nevanlinna-Pick and Carath?odory-Fej?r type are included as well as moment problems and problems of integral representation in assorted settings. The major themes cover applications of the Potapov method of fundamental matrix inequalities, multiplicative decompositions of J-inner matrix valued functions, the abstract interpolation problem, canonical systems of differential equations and interpolation in spaces with an indefinite metric. This book should appeal to a wide range of readers: mathematicians specializing in pure and applied mathematics and engineers who work in systems theory and control. The book will be of use to graduate students and mathematicians interested in functional analysis.
Content:
Front Matter....Pages I-XXII
Vladimir Petrovich Potapov as remembered by colleagues, friends and former students....Pages 1-18
On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc....Pages 19-35
On tangential interpolation in reproducing kernel Hilbert modules and applications....Pages 37-68
Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions....Pages 69-91
The indefinite metric in the Schur interpolation problem for analytic functions. IV....Pages 93-104
Bitangential interpolation for upper triangular operators....Pages 105-142
Bitangential interpolation for triangular operators when the Pick operator is strictly positive....Pages 143-164
Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class....Pages 165-184
On recovering a multiplicative integral from its modulus....Pages 185-193
On Schur functions and Szeg? orthogonal polynomials....Pages 195-203
Hilbert spaces of entire functions as a J theory subject....Pages 205-251
On transformations of Potapov’s fundamental matrix inequality....Pages 253-281
An abstract interpolation problem and the extension theory of isometric operators....Pages 283-298
On the theory of matrix-valued functions belonging to the Smirnov class....Pages 299-350
On the theory of entire matrix-functions of exponential type....Pages 351-359
Analogs of the Nehari and Sarason theorems for character-automorphic functions and some related questions....Pages 361-371
The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators....Pages 373-390
Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner matrix functions....Pages 391-396
On a criterion of positive definiteness....Pages 397-417
Matrix boundary value problems with eigenvalue dependent boundary conditions (the linear case)....Pages 419-451
Weyl-Titchmarsh functions of the canonical periodical system of differential equations....Pages 453-462
On boundary values of functions regular in a disk....Pages 463-479
Back Matter....Pages 481-494
....Pages 495-498