
Factorization, Singular Operators and Related Problems
By: Stefan Samko (Editor), Amarino Lebre (Editor), António F. dos Santos (Editor)
Hardcover | 31 July 2003
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360 Pages
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| Preface | p. ix |
| Foreword | p. xiii |
| A few words about Georgii Litvinchuk | p. xvii |
| Contributed Papers | |
| Singular Integrals Along Flat Curves with Kernels in the Hardy Space H[superscript 1] (S[superscript n-1]) | p. 1 |
| Introduction and statement of results | p. 1 |
| The Hardy space H[superscript 1] (S[superscript n-1]) | p. 3 |
| Preparation | p. 4 |
| Proof of main results | p. 6 |
| On Functional Equations with Operator Coefficients | p. 13 |
| Introduction | p. 13 |
| C*-algebras, generated by dynamical systems. The isomorphism theorem | p. 14 |
| The symbolic calculus for FPDO | p. 16 |
| The invertibility conditions for functional operators. The hyperbolic approach | p. 17 |
| The case of a finite group. Formulas for the index | p. 19 |
| The essential spectra of weighted shift operators | p. 20 |
| Elliptic Systems with Almost Regular Coefficients: Singular Weight Integral Operators | p. 25 |
| Introduction | p. 25 |
| Definitions. Embedding theorems | p. 26 |
| Integral equations. Weight integral operators | p. 31 |
| Boundary value problems for generalized analytic functions | p. 38 |
| Smoothness of quasi-conformal mappings | p. 39 |
| Toeplitz Matrices with Slowly Growing Pseudospectra | p. 43 |
| Introduction and Main Results | p. 43 |
| Toeplitz determinants | p. 45 |
| Slow growth of the resolvent norm | p. 51 |
| A Numerical Procedure for the Inverse Sturm-Liouville Operator | p. 55 |
| Introduction | p. 55 |
| Formulation of the method | p. 56 |
| Some examples | p. 59 |
| Using different gradients | p. 60 |
| Conclusion | p. 63 |
| A Geometrical Proof of a Theorem of Crum | p. 65 |
| Introduction | p. 65 |
| The strongly continous unitary group associated to f | p. 66 |
| Construction of the function f[superscript c] | p. 69 |
| Positive definiteness of f[superscript o] | p. 71 |
| Localization and Minimal Normalization of some Basic Mixed Boundary Value Problems | p. 73 |
| Introduction to mixed boundary value problems and normalization | p. 74 |
| Associated operators | p. 77 |
| Localization | p. 79 |
| Reduction to semi-homogeneous problems | p. 83 |
| The Fredholm property | p. 86 |
| Normalization - the basic idea | p. 89 |
| Minimal normalization in the scalar case | p. 94 |
| Concluding remarks | p. 97 |
| Factorization of some Classes of Matrix Functions and the Resolvent of a Hankel Operator | p. 101 |
| Introduction | p. 101 |
| Factorization of a class of hermitian matrix functions | p. 103 |
| The resolvent of a Hankel operator | p. 106 |
| Compactness of Commutators Arising in the Fredholm Theory of Singular Integral Operators with Shifts | p. 111 |
| Introduction | p. 111 |
| Preliminaries | p. 113 |
| Compactness of commutators on L[superscript 2] | p. 118 |
| Compactness of commutators on rearrangement-invariant spaces | p. 125 |
| Some corollaries | p. 125 |
| Some Problems in the Theory of Integral and Differential Equations of Fractional Order | p. 131 |
| Introduction | p. 131 |
| Laplace transform method | p. 132 |
| Operational calculus method | p. 137 |
| Compositional method | p. 140 |
| Problems and new trends of research | p. 144 |
| Fractional Differential Equations: A Emergent Field in Applied and Mathematical Sciences | p. 151 |
| Introduction | p. 152 |
| The Complexity Systems | p. 154 |
| Fractional Integral and Fractional Derivative Operators | p. 158 |
| A New Model for the Super-Diffusion Processes | p. 161 |
| Boundary Value Problems for Analytic and Harmonic Functions of Smirnov Classes in Domains with Non-Smooth Boundaries | p. 175 |
| The Riemann Problem with Boundary Values from the Zygmund Class | p. 177 |
| The Dirichlet Problem for Harmonic Functions from the Smirnov Classes ep (D) and ep (D, [rho]) | p. 182 |
| The Dirichlet Problem in the Class e 1 (D) when the Boundary Function Belongs to the Zygmund Class | p. 189 |
| An Estimate for the Dimension of the Kernel of a Singular Operator with a non-Carleman Shift | p. 197 |
| Introduction | p. 197 |
| An estimate for dim ker T | p. 198 |
| On the Solution of Integral Equations on the Circular Disk by Use of Orthogonal Polynomials | p. 205 |
| Introduction | p. 205 |
| Basic results | p. 207 |
| The fully discretised Galerkin method | p. 212 |
| Error estimates | p. 215 |
| Singular and Fredholm Integral Equations for Dirichlet Boundary Problems for Axial-Symmetric Potential Fields | p. 219 |
| Introduction | p. 219 |
| Preliminary notes and notation | p. 221 |
| Dirichlet boundary problem for the axial-symmetric potential | p. 222 |
| Dirichlet boundary problem for the Stokes flow function | p. 228 |
| On the Analyticity of the Schwarz Operator with Respect to a Curve | p. 237 |
| Introduction | p. 237 |
| Preliminaries and notation | p. 240 |
| Real analyticity of the modified Schwarz operator | p. 245 |
| Regularity of another variants of the Schwarz operator | p. 251 |
| Integral Operators with Shifts on Homogeneous Groups | p. 255 |
| Introduction | p. 255 |
| The limit operators method | p. 256 |
| Operators on homogeneous groups | p. 259 |
| Fredholmness of convolution operators with shifts | p. 264 |
| On the Algebra Generated by a Poly-Bergman Projection and a Composition Operator | p. 273 |
| Introduction | p. 273 |
| Symbol algebra of R n,A = R(CI; B n, B n,A) | p. 275 |
| Symbol algebra of R n = R(C(G)I; B n, W B n W) | p. 281 |
| Symbol algebra of R n,W = R(C(G)I; B n, W) | p. 284 |
| Proof of Theorem 1.1 | p. 286 |
| How to Compute the Partial Indices of a Regular and Smooth Matrix-Valued Function? | p. 291 |
| Introduction | p. 291 |
| Toeplitz operators and their finite sections | p. 292 |
| Modified finite sections | p. 295 |
| Speed of convergence | p. 296 |
| Collocation-based approximations | p. 298 |
| The Multiplicative and Spectral Structure of Analytic Operator-Valued Functions | p. 301 |
| Introduction | p. 301 |
| Limiting values of multiplicative integrals | p. 302 |
| The case of the derivative in the Hardy class | p. 312 |
| Toeplitz Operators on the Bergman Space | p. 315 |
| Introduction | p. 315 |
| Commutative algebras of Toeplitz operators | p. 316 |
| Bergman space structure and spectral form of special classes of Toeplitz operators | p. 318 |
| Unbounded symbols | p. 322 |
| Commutator properties and representations of C*-algebras | p. 324 |
| Dynamics of properties of Toeplitz operators | p. 326 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9781402014079
ISBN-10: 1402014074
Published: 31st July 2003
Format: Hardcover
Language: English
Number of Pages: 360
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 25.4 x 16.51 x 2.54
Weight (kg): 0.69
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