Modern Operator Theory And Applications

This volume is dedicated to the eminent Russian mathematician Igor Borisovich Simonenko on the occasion of his 70th birthday. The contributions are written by leading experts and present the state of the art in a number of areas originally initiated in pioneer works by I. B. Simonenko. Among the topics covered are Fredholm theory for singular integral and convolution operators, estimates for singular integral operators on Carleson curves acting in Lp spaces with variable exponents, the finite section method for band-dominated and Toeplitz operators, Szegö-type theorems, and the averaging method for nonlinear equations. The book testifies to the wide mathematical interest of I. B. Simonenko and includes a biography, his list of publications and a list of his Ph.D. students.

Portrait of Igor Borisovich Simonenko	p. vii
Editorial Introduction	p. viii
Introduction
Life and Work of Igor Borisovich Simonenko	p. 1
Operators of Local Type and Singular Integral Operators	p. 2
An Averaging Method and its Application to Hydrodynamics Problems	p. 5
List of Ph.D., whose Supervisor was LB. Simonenko	p. 12
List of Ph.D., whose co-supervisor was LB. Simonenko	p. 13
List of D.Sc, whose advisor was LB. Simonenko	p. 13
Principal Publications of LB. Simonenko	p. 13
Contributions
Coefficients Averaging for Functional Operators Generated by Irrational Rotation	p. 27
On the Verification of Linear Equations and the Identification of the Toeplitz-plus-Hankel Structure	p. 43
Asymmetric Factorizations of Matrix Functions on the Real Line	p. 53
On the Structure of the Square of a C₀(1) Operator	p. 75
On the Connection Between the Indices of a Block Operator Matrix and of its Determinant	p. 85
Quasi-commutativity of Entire Matrix Functions and the Continuous Analogue of the Resultant	p. 101
Double Barrier Options Under Lévy Processes	p. 107
A Local-trajectory Method and Isomorphism Theorems for Nonlocal C*-algebras	p. 137
Boundedness in Lebesgue Spaces with Variable Exponent of the Cauchy Singular Operator on Carleson Curves	p. 167
On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces	p. 187
Finite Sections of Band-dominated Operators with Almost Periodic Coefficients	p. 205
On the Toeplitz Operators with Piecewise Continuous Symbols on the Bergman Space	p. 229
Asymptotics of a Class of Operator Determinants	p. 249
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