Factorization, singular operators and related problems : proceedings of the conference in honour of Professor Georgii Litvinchuk / edited by Stefan Samko, Amarino Lebre and António F. dos Santos.

Format:

Book

Contributor:

Litvinchuk, G. S. (Georgiĭ Semenovich), 1931-

Samko, S. G. (Stefan Grigorʹevich)

Lebre, Amarino

Santos, António Ferreira dos, 1939-

Rosengarten Family Fund.

Language:

English

Subjects (All):

Integral operators.

Factorization of operators--Congresses.

Factorization of operators.

Factorization (Mathematics)--Congresses.

Factorization (Mathematics).

Genre:

Conference papers and proceedings.

Festschriften.

Physical Description:

xviii, 333 pages : illustrations ; 25 cm

Place of Publication:

Dordrecht ; Boston ; London : Kluwer Academic Publishers, [2003]

Summary:

The International Conference on Factorization, Singular Operators and Related Problems held from January 28 to February 1, 2002, at the University of Madeira, Funchal, Portugal, was dedicated to mark Professor Georgii Litvinchuk's 70th birthday. Experts in various fields came to this conference to pay tribute to the great achievements of Professor Georgii Litvinchuk in the development of various topics of operator theory. The main topics of the conference were in the theory of singular type operators and in factorization problems, but other topics such as potential theory, fractional calculus and others were also presented. The 21 articles published in this book will be of great interest to researchers in Operator Theory, Real and Complex Analysis, Functional and Harmonic Analysis, Potential Theory, Fractional Calculus and others, as well as to graduate students requiring the most up-to-date results.

Contents:

Contributed Papers

Singular Integrals Along Flat Curves with Kernels in the Hardy Space H[superscript 1] (S[superscript n-1]) / Ahmad Al-Salman, Hussain Al-Qassem 1

1 Introduction and statement of results 1

2 The Hardy space H[superscript 1] (S[superscript n-1]) 3

3 Preparation 4

4 Proof of main results 6

On Functional Equations with Operator Coefficients / Anatolij Antonevich 13

2 C*-algebras, generated by dynamical systems. The isomorphism theorem 14

3 The symbolic calculus for FPDO 16

4 The invertibility conditions for functional operators. The hyperbolic approach 17

5 The case of a finite group. Formulas for the index 19

6 The essential spectra of weighted shift operators 20

Elliptic Systems with Almost Regular Coefficients: Singular Weight Integral Operators / Stanislav Antontsev 25

2 Definitions. Embedding theorems 26

3 Integral equations. Weight integral operators 31

4 Boundary value problems for generalized analytic functions 38

5 Smoothness of quasi-conformal mappings 39

Toeplitz Matrices with Slowly Growing Pseudospectra / Albrecht Bottcher, Sergei Grudsky 43

2 Toeplitz determinants 45

3 Slow growth of the resolvent norm 51

A Numerical Procedure for the Inverse Sturm-Liouville Operator / B. Malcolm Brown, Valentin Samko, Ian Knowles, Marco Marletta 55

2 Formulation of the method 56

4 Using different gradients 60

A Geometrical Proof of a Theorem of Crum / Ramon Bruzual, Marisela Dominguez 65

2 The strongly continous unitary group associated to f 66

3 Construction of the function f[superscript c] 69

4 Positive definiteness of f[superscript o] 71

Localization and Minimal Normalization of some Basic Mixed Boundary Value Problems / Luis P. Castro, Roland Duduchava, Frank-Olme Speck 73

1 Introduction to mixed boundary value problems and normalization 74

2 Associated operators 77

3 Localization 79

4 Reduction to semi-homogeneous problems 83

5 The Fredholm property 86

7 Minimal normalization in the scalar case 94

Factorization of some Classes of Matrix Functions and the Resolvent of a Hankel Operator / Ana C. Conceicao, Viktor G. Kravchenko, Francisco S. Teixeira 101

2 Factorization of a class of hermitian matrix functions 103

3 The resolvent of a Hankel operator 106

Compactness of Commutators Arising in the Fredholm Theory of Singular Integral Operators with Shifts / Alexei Karlovich, Yuri Karlovich 111

3 Compactness of commutators on L[superscript 2] 118

4 Compactness of commutators on rearrangement-invariant spaces 125

5 Some corollaries 125

Some Problems in the Theory of Integral and Differential Equations of Fractional Order / Anatoly A. Kilbas 131

2 Laplace transform method 132

3 Operational calculus method 137

4 Compositional method 140

5 Problems and new trends of research 144

Fractional Differential Equations: A Emergent Field in Applied and Mathematical Sciences / Anatoly A. Kilbas, Hari M. Srivastava, Juan J. Trujillo 151

2 The Complexity Systems 154

3 Fractional Integral and Fractional Derivative Operators 158

4 A New Model for the Super-Diffusion Processes 161

Boundary Value Problems for Analytic and Harmonic Functions of Smirnov Classes in Domains with Non-Smooth Boundaries / Vakhtang Kokilashvili, Zurab Meshveliani, Vakhtang Paatashvili 175

1 The Riemann Problem with Boundary Values from the Zygmund Class 177

2 The Dirichlet Problem for Harmonic Functions from the Smirnov Classes ep (D) and ep (D, [rho]) 182

3 The Dirichlet Problem in the Class e 1 (D) when the Boundary Function Belongs to the Zygmund Class 189

An Estimate for the Dimension of the Kernel of a Singular Operator with a non-Carleman Shift / Viktor G. Kravchenko, Rui C. Marreiros 197

2 An estimate for dim ker T 198

On the Solution of Integral Equations on the Circular Disk by Use of Orthogonal Polynomials / Frank Penzel 205

3 The fully discretised Galerkin method 212

4 Error estimates 215

Singular and Fredholm Integral Equations for Dirichlet Boundary Problems for Axial-Symmetric Potential Fields / Sergiy Plaksa 219

3 Dirichlet boundary problem for the axial-symmetric potential 222

4 Dirichlet boundary problem for the Stokes flow function 228

On the Analyticity of the Schwarz Operator with Respect to a Curve / Luca Preciso, Sergei Rogosin 237

3 Real analyticity of the modified Schwarz operator 245

4 Regularity of another variants of the Schwarz operator 251

Integral Operators with Shifts on Homogeneous Groups / Vladimir S. Rabinovich, Steffen Roch 255

2 The limit operators method 256

3 Operators on homogeneous groups 259

4 Fredholmness of convolution operators with shifts 264

On the Algebra Generated by a Poly-Bergman Projection and a Composition Operator / Josue Ramirez, Ilya M. Spitkovsky 273

2 Symbol algebra of R n,A = R(CI; B n, B n,A) 275

3 Symbol algebra of R n = R(C(G)I; B n, W B n W) 281

4 Symbol algebra of R n,W = R(C(G)I; B n, W) 284

5 Proof of Theorem 1.1 286

How to Compute the Partial Indices of a Regular and Smooth Matrix-Valued Function? / Bernd Silbermann 291

2 Toeplitz operators and their finite sections 292

3 Modified finite sections 295

4 Speed of convergence 296

5 Collocation-based approximations 298

The Multiplicative and Spectral Structure of Analytic Operator-Valued Functions / Anna Tarasenko 301

2 Limiting values of multiplicative integrals 302

3 The case of the derivative in the Hardy class 312

Toeplitz Operators on the Bergman Space / Nikolai Vasilevski 315

2 Commutative algebras of Toeplitz operators 316

3 Bergman space structure and spectral form of special classes of Toeplitz operators 318

4 Unbounded symbols 322

5 Commutator properties and representations of C*-algebras 324

6 Dynamics of properties of Toeplitz operators 326.

Notes:

Includes bibliographical references.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

1402014074

OCLC:

52257946