Modern Operator Theory and Applications

This volume is dedicated to the eminent Russian mathematician Igor Borisovich Simonenko on the occasion of his 70th birthday. It consists of a selection of 15 original contributions written by leading experts in operator theory. The topics reflect the wide range and the rich variety of areas of interests, achievements and influence of I.B. Simonenko. The book also includes his biography, the complete list of publications and a list of his Ph.D. students.

Among the topics covered are functional, Toeplitz and Toeplitz plus Hankel, local and nonlocal, singular integral and convolution operators, and continuous analogs of resultant operators. The contributions analyze and solve problems of factorization, irreducibility, asymptotics of determinants, finite sections, and index problems for different types of operators. Applications concern problems in financial mathematics and hydrodynamics.

The book will be of interest to a wide audience of pure and applied mathematicians.

Résumé
(jointly with V.P. Zakharyuta and V.I. Yudovich), including a calculation of the capacity of condensers of complex form and dielectric materials with complex structure. In 1967, at the age of 32, six years after he defended his Ph.D. thesis, I.B. - monenko defended his thesis for a degree of Doctor of Science. In this thesis, entitled Operators of local type and some other problems of the theory of linear operators, he sharply turned towards the wide usage of the general methods of functional analysis. In 1971 professor I.B. Simonenko became the head of the - merical Mathematics Chair. The following year this chair was split into two; I.B. became the head of one of them, the Chair of Algebra and Discrete Mathematics. The Chair of Algebra and Discrete Mathematics can be rightfully called the Chair of I.B. Simonenko. Here he worked together with his colleagues, students, and the students of his students. Here he fully developed his teaching talent. He lectured on Algebra and geometry, Mathematical logic, Discrete mathem- ics, and Mathematical analysis.

Contenu
Coefficients Averaging for Functional Operators Generated by Irrational Rotation.- On the Verification of Linear Equations and the Identification of the Toeplitz-plus-Hankel Structure.- Asymmetric Factorizations of Matrix Functions on the Real Line.- On the Structure of the Square of a C 0(1) Operator.- On the Connection Between the Indices of a Block Operator Matrix and of its Determinant.- Quasi-commutativity of Entire Matrix Functions and the Continuous Analogue of the Resultant.- Double Barrier Options Under Lévy Processes.- A Local-trajectory Method and Isomorphism Theorems for Nonlocal C*-algebras.- Boundedness in Lebesgue Spaces with Variable Exponent of the Cauchy Singular Operator on Carleson Curves.- On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces.- Finite Sections of Band-dominated Operators with Almost Periodic Coefficients.- On the Toeplitz Operators with Piecewise Continuous Symbols on the Bergman Space.- Asymptotics of a Class of Operator Determinants.