By D. Z. Arov (auth.), I. Gohberg, L. A. Sakhnovich (eds.)

This publication is devoted to the reminiscence of an exceptional mathematician and character, Vladimir Petrovich Potapov, who made vital contributions to and exerted substantial impression within the components of operator thought, advanced research and their issues of juncture. The publication commences with insightful biographical fabric, after which provides a suite of papers on diverse features of operator thought and complicated research protecting these contemporary achievements of the Odessa-Kharkov university within which Potapov was once very energetic. The papers care for interrelated difficulties and techniques. the most subject matters are the multiplicative constitution of contractive matrix and operator capabilities, operators in areas with indefinite scalar items, inverse difficulties for structures of differential equations, interpolation and approximation difficulties for operator and matrix features. The e-book will attract a large staff of mathematicians and engineers, and lots more and plenty of the cloth can be utilized for complex classes and seminars.

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He successfully solved this problem in [29]. I. P. Fedcina generalized his result on the tangential Nevanlinna-Pick problem in [30]. But this problem was connected with Blaschke-Potapov products for which the elementary multipliers have poles in one halfplane, right or left. When these poles are in both half-planes, such Blaschke-Potapov products are connected with the bitangential Nevanlinna-Pick problem in which data are given for tangential interpolation of Z(A) and Z*(A). In the class Bnxm such bitangential problems may be formulated in this way: Let So E Bnxm' bl E B n, b2 E Bm be given, where bl and b2 are Blaschke-Potapov products.

30J 1. P. Fedcina, The tangential Nevanlinna-Pick problem with multiple points, Akad. Nauk Armjan. SSR Dokl. 61 (1975),214-218. MR 53#13576. [31J D. Z. Arov and L. A. Simakova, The boundary values of a convergent sequence of J -contractive matrix-valued functions, Mat. Zametki 19, no. 4, (1976), 491500. MR 58#6278. [32J D. Z. Arov, ,-generating matrices, j -inner matrix functions and related extrapolation problems. I Teor. Funktsii Funktsional. Anal. i Prilozhen. 51 (1989), 61-67; Part II, ibid.

42] D. Z. Arov and M. G. KreIn, Calculation of entropy functionals and their minima in indeterminate continuation problems, Acta Sci. Math. (Szeged) 45 (1983), 33-50. MR 84h:30050. [43] D. Z. Arov, The generalized bitangential Caratheodory-Nevanlinna-Pick problem and (j,J)-inner matrix functions, Internat. Workshop on Algorithms and Parallel VLSI Architectures, June 10-16, 1990, Abbaye des Premontres, Pont-a-Mousson-France, Part B, 179-183. [44] D. Z. Arov, (j,J)-inner matrix functions and the generalized bitangential Caratheodory-Nevanlinna-Pick-Krdn problem, WOTCA Workshop on Operators and Complex Analysis, June 11-14, 1991, 4-5, Abstracts, Hokkaido University, Sapporo, Japan.