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El. knyga: Topics in Interpolation Theory

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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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Springer Book Archives
Vladimir Petrovich Potapov, as remembered by colleagues, friends and
former students.- On a minimum problem in function theory and the number of
roots of an algebraic equation inside the unit disc.- On tangential
interpolation in reproducing kernel Hilbert modules and applications.- Notes
on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna
functions.- The indefinite metric in the Schur interpolation problem for
analytic functions, IV.- Bitangential interpolation for upper triangular
operators.- Bitangential interpolation for upper triangular operators when
the Pick operator is strictly positive.- Integral representations of a pair
of nonnegative operators and interpolation problems in the Stieltjes class.-
On recovering a multiplicative integral from its modulus.- On Schur functions
and Szegö orthogonal polynomials.- Hilbert spaces of entire functions as a J
theory subject.- On transformations of Potapovs fundamental matrix
inequality.- An abstract interpolation problem and the extension theory of
isometric operators.- On the theory of matrix-valued functions belonging to
the Smirnov class.- Integral representation of function of class Ka.- On the
theory of entire matrix-functions of exponential type.- Analogs of Nehari and
Sarason theorems for character-automorphic functions and some related
questions.- The Blaschke-Potapov factorization theorem and the theory of
nonselfadjoint operators.- Weyl matrix circles as a tool for uniqueness in
the theory of multiplicative representation of J-inner functions.- On a
criterion of positive definiteness.- Matrix boundary value problems with
eigenvalue dependent boundary conditions (The linear case).- Weyl-Titchmarsh
functions of the canonical periodical system of differential equations.- On
boundary values offunctions regular in a disk.
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