Modern Operator Theory and Applications

1. Front Matter

   Pages i-vii

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2. Introduction

   Pages 1-26

3. Coefficients Averaging for Functional Operators Generated by Irrational Rotation

   • A. B. Antonevich

   Pages 27-41

4. On the Verification of Linear Equations and the Identification of the Toeplitz-plus-Hankel Structure

   • Albrecht Böttcher, David Wenzel

   Pages 43-51

5. Asymmetric Factorizations of Matrix Functions on the Real Line

   • L. P. Castro, R. Duduchava, F. -O. Speck

   Pages 53-74

6. On the Structure of the Square of a C ₀(1) Operator

   • Ronald G. Douglas, Ciprian Foias

   Pages 75-84

7. On the Connection Between the Indices of a Block Operator Matrix and of its Determinant

   • Israel Feldman, Nahum Krupnik, Alexander Markus

   Pages 85-100

8. Quasi-commutativity of Entire Matrix Functions and the Continuous Analogue of the Resultant

   • I. Gohberg, M. A. Kaashoek, L. Lerer

   Pages 101-106

9. Double Barrier Options Under Lévy Processes

   • Sergei M. Grudsky

   Pages 107-135

10. A Local-trajectory Method and Isomorphism Theorems for Nonlocal C*-algebras

    • Yu. I. Karlovich

    Pages 137-166

11. Boundedness in Lebesgue Spaces with Variable Exponent of the Cauchy Singular Operator on Carleson Curves

    • Vakhtang Kokilashvili, Vakhtang Paatashvili, Stefan Samko

    Pages 167-186

12. On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces

    • V. B. Levenshtam

    Pages 187-203

13. Finite Sections of Band-dominated Operators with Almost Periodic Coefficients

    • Vladimir S. Rabinovich, Steffen Roch, Bernd Silbermann

    Pages 205-228

14. On the Toeplitz Operators with Piecewise Continuous Symbols on the Bergman Space

    • N. Vasilevski

    Pages 229-248

15. Asymptotics of a Class of Operator Determinants

    • Harold Widom

    Pages 249-256

(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”.

• C*-algebra
• Carleson curve
• Toeplitz operator
• band-dominated operator
• convolution
• differential equation
• finite sections method
• operator theory
• singular integral operator

• Mechanical-Mathematics Department, Rostov State University, Rostov-on-Don, Russia

  Yakob M. Erusalimsky

• School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

  Israel Gohberg

• Departamento de Matemáticas, CINVESTAV, Mexico, D.F., Mexico

  Sergei M. Grudsky, Nikolai Vasilevski

• Instituto Politecnico Nacional, ESIME Zacatenco, Mexico, D. F., Mexico

  Vladimir Rabinovich

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