Topics in Interpolation Theory

✍ Scribed by Moshe Livšic (auth.), H. Dym, V. Katsnelson, B. Fritzsche, B. Kirstein (eds.)

• Publisher: Birkhäuser Basel
• Year: 1997
• Tongue: English
• Leaves: 508
• Series: Operator Theory Advances and Applications 95
• Edition: 1
• Category: Library

✦ Synopsis

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).

✦ Table of Contents

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 Szegő 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
Integral representation of functions of class K a ....Pages 351-359
On the theory of entire matrix-functions of exponential type....Pages 361-371
Analogs of the Nehari and Sarason theorems for character-automorphic functions and some related questions....Pages 373-390
The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators....Pages 391-396
Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J -inner matrix functions....Pages 397-417
On a criterion of positive definiteness....Pages 419-451
Matrix boundary value problems with eigenvalue dependent boundary conditions (the linear case)....Pages 453-462
Weyl-Titchmarsh functions of the canonical periodical system of differential equations....Pages 463-479
On boundary values of functions regular in a disk....Pages 481-494
Back Matter....Pages 495-498

✦ Subjects

Mathematics, general