Modern Operator Theory and Applications (eBook)

The Igor Borisovich Simonenko Anniversary Volume

Yakob M. Erusalimskii, Israel Gohberg, Sergei M. Grudsky, Vladimir Rabinovich, Nikolai Vasilevski (Herausgeber)

eBook Download: PDF

2007
VII, 256 Seiten
Springer Basel (Verlag)
978-3-7643-7737-3 (ISBN)

Infos

This volume is dedicated to the eminent Russian mathematician I.B. Simonenko on the occasion of his 70th birthday. It presents recent results in 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 sections method for band-dominated and Toeplitz operators, Szegö type theorems, the averaging method for nonlinear equations, among others.

Inhalt

Contents 6
Introduction 9
Life and Work of Igor Borisovich Simonenko 9
Operators of Local Type and Singular Integral Operators 10
An Averaging Method and its Application 13
to Hydrodynamics Problems 13
List of Ph.D., whose supervisor was I.B. Simonenko 20
List of Ph.D., whose co-supervisor was I.B. Simonenko 21
List of D.Sc., whose advisor was I.B. Simonenko 21
Principal Publications of I.B. Simonenko 21
Coefficients Averaging for Functional Operators Generated by Irrational Rotation 35
1. Introduction 35
2. Weighted composition operators generated by irrational rotation 37
3. Two-term functional operators, generated 42
by an irrational rotation 42
References 48
On the Verification of Linear Equations and the Identification of the Toeplitz-plus-Hankel Structure 51
1. Introduction 51
2. General homogeneous linear equations 53
3. The Toeplitz-plus-Hankel structure 55
4. General inhomogeneous linear equations 57
5. Toeplitz-plus-Hankel matrices again 58
References 59
Asymmetric Factorizations of Matrix Functions on the Real Line 61
1. Introduction 61
2. Classical factorization 62
3. Asymmetric and anti-symmetric factorizations 68
A. Appendix 74
References 81
On the Structure of the Square of a Co (1) Operator 83
References 92
On the Connection Between the Indices of a Block Operator Matrix and of its Determinant 93
1. Introduction 93
2. Counterexamples 95
3. Preliminaries 97
4. 99
block operator matrices 99
5. The general case 103
References 107
Quasi-commutativity of Entire Matrix Functions and the Continuous Analogue of the Resultant 109
References 114
Double Barrier Options Under L ´ evy Processes 115
1. Introduction 115
2. Auxiliary material 116
3. 120
Convolution 120
equation and classes of symbols 120
4. Reducing to modi.ed Wiener-Hopf equation. 125
Necessary information from Toeplitz operator theory 125
5. Unique solvability of the modi.ed Wiener-Hopf equation 129
in the space 129
6. Unique solvability of the problem (2.10)–(2.12) 135
and the price of the double barrier option 135
7. Stability of the solution with respect to small perturbations 137
of the characteristic function 137
8. Conclusion 140
References 141
A Local-trajectory Method and Isomorphism Theorems for Nonlocal C*-algebras 145
1. Introduction 145
2. Crossed products and their regular representations 147
3. Isomorphism theorems 151
4. Trajectorial localization 154
5. The isomorphism theorem and trajectorial localization again 167
References 173
Boundedness in Lebesgue Spaces with Variable Exponent of the Cauchy Singular Operator on Carleson Curves 175
1. Introduction 175
2. De.nitions 176
3. The main statements 177
4. Preliminaries 179
5. Auxiliary statements 180
6. Proof of Theorem A 181
7. Proof of Theorem B 188
8. Proof of Theorem C 191
9. Appendices 192
References 193
On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces 195
1. Introduction 195
2. Statement of the results 196
3. Proof of the theorems 200
References 210
Finite Sections of Band-dominated Operators with Almost Periodic Coefficients 213
1. Introduction 213
2. Limit operators of band-dominated operators 217
with almost periodic coe.cients 217
3. Band-dominated operators with almost 218
periodic coe.cients on 218
4. Distinguished .nite sections methods 220
5. The algebra of the .nite sections method 224
6. Spectral approximation 227
7. Test calculations 230
References 235
On the Toeplitz Operators with Piecewise Continuous Symbols on the Bergman Space 237
1. Introduction 237
2. Preliminaries 239
3. Essential and local spectra 244
5. Boundary piecewise continuous functions 253
References 255
Asymptotics of a Class of Operator Determinants 257
1. Introduction and statement of the result 257
2. Derivation of the result 260
3. Final remarks 262
References 264

Produkt-Details

• Erscheint lt. Verlag: 6.3.2007
• Reihe/Serie: Operator Theory: Advances and Applications
• Reihe/Serie: Operator Theory: Advances and Applications
• Zusatzinfo: VII, 256 p.
• Verlagsort: Basel
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: band-dominated operator • C*-algebra • Carleson curve • convolution • differential equation • finite sections method • operator theory • singular integral operator • Toeplitz operator
• ISBN-10: 3-7643-7737-2 / 3764377372
• ISBN-13: 978-3-7643-7737-3 / 9783764377373