Singular Integral Operators, Factorization and Applications

, by Kaashoek, M. A.; Lebre, Amarino Brites; Dos Santos, Antonio Ferreira; Speck, Frank-Olme; Bottcher, Albrecht

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ISBN: 9783764369477 | 3764369477
Cover: Hardcover
Copyright: 6/1/2003

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This book contains the proceedings of the International Workshop on Operator Theory and Applications held in Faro, Portugal, September 12 to 15, 2000. It includes 20 selected articles centered on the analysis of various classes of singular operators, the factorization of operator and matrix functions, algebraic methods in approximation theory, and applications in diffraction theory. Some papers are related to topics from fractional calculus, complex analysis, operator algebras, and partial differential equations.

Editorial Introduction

Note on the Memory of Professor Erhard Meister

xiii

Program of IWOTA-Portugal 2000

xiv

List of Participants

Covariant Symbolic Calculi on Real Symmetric Domains

by JONATHAN ARAZY AND HARALD UPMEIER

1. Introduction

(1)

2. Real symmetric domains

(3)

3. Quantization Hilbert spaces

(4)

4. Covariant symbolic calculi on real symmetric domains

(5)

5. The Toeplitz-Berezin calculus

(12)

References

(3)

Singular Integral operators with Piecewise Almost Periodic Coefficients and Carleman Shift

by M. AMI LIA BASTOS, ANTÓNIO BRAVO AND YURI KARLOVICH

1. Introduction

(2)

2. Preliminaries

(2)

3. The algebra of singular integral operators with piecewise continuous coefficients

(4)

4. The Fredholm study of operators with semi-almost periodic coefficients

(8)

5. Singular integral operators with piecewise almost periodic coefficients

(6)

6. Fredholmness of singular integral operators with Carleman shift and piecewise almost periodic coefficients

(5)

References

(3)

On the Essential Spectrum of Toeplitz Operators with Semi-Almost Periodic Symbols

by ALBRECHT BÖTTCHER, SERGEI GRUDSKY AND ILYA SPITKOVSKY

1. Introduction and main results

(4)

2. Sarason's criterion

(1)

3. The local shape of the essential spectrum

(1)

4. Essential spectra of prescribed local shapes

(5)

5. Essential spectra of prescribed global shapes

(4)

6. Separated almost periodic representatives

(2)

References

(3)

Well-Posedness of Diffraction Problems Involving n Coplanar Strips

by LUÍS PINHEIRO DE CASTRO AND FRANK-OLME SPECK

1. Introduction

(1)

2. Formulation of the problem

(2)

3. Relations with Wiener-Hopf operators

(3)

4. Sufficient conditions for the invertibility

(3)

5. Example: The Rawlins problem for n strips

(2)

References

(2)

Factorization of Matrix Functions and the Resolvents of Certain Operators

by ANA CONCEIÇAO, VIKTOR KRAVCHENKO AND FRANCISCO TEIXEIRA

1. Introduction

(1)

2. Preliminaries

(1)

3. Resolvents of N_ and N+ through the factorization of A7

(1)

4. Factorization of A7 through the resolvent of N_ and N+

(6)

References

100

(1)

Finite Difference Cauchy-Riemann Operators and Their Fundamental Solutions in the Complex Case

by KLAUS GURLEBECK AND ANGELA HOMMEL

1. Introduction

101

(1)

2. Cauchy-Riemann operators and fundamental solutions in the complex case

102

(1)

3. Discrete theory

103

(11)

References

114

(3)

Factorization Theorem for the Transfer Function Associated with an Unbounded Non-Self-Adjoint 2 x 2 Operator Matrix

by VOLKER HARDT, REINHARD MENNICKEN AND ALEXANDER K. MOTOVILOV

1. Introduction

117

(2)

2. Analytic continuation

119

(2)

3. The transformation equations

121

(3)

4. Factorization

124

(5)

5. An example

129

(2)

References

131

(2)

Boundedness of Some Convolution and Twisted Convolution Operators

by ALEXEY N. KARAPETYANTS AND ENRIQUE RAMÍREZ DE ARELLANO

1. Introduction

133

(2)

2. Integral representations for the operators Ao, Bo and some properties of the kernel Oo(x)

135

(3)

3. Boundedness of convolution operators

138

(1)

4. Boundedness of twisted convolution operators

139

(3)

5. Concluding remarks

142

(1)

References

143

(4)

Invertibility of Functional Operators with Slowly Oscillating Non-Carleman Shifts

by ALEXEI KARLOVICH, YURI KARLOVICH AND AMARINO LEBRE

1. Introduction

147

(3)

2. Sufficient conditions for one-sided invertibility

150

(5)

3. Slowly oscillating functions and shifts

155

(4)

4. Limit operators for a functional operator

159

(9)

5. Necessary conditions for invertibility

168

(5)

References

173

(2)

Hadamard-Type Integral Equations and Fractional Calculus Operators

by ANATOLY A. KILBAS

1. Introduction

175

(3)

2. Hadamard-type fractional integrals and derivatives in Xu(a,b)

178

(3)

3. Hadamard-type integral equations in Xu(a, b)

181

(5)

4. Hadamard-type integral equations in Xu(a, b) in the case 0 less than o less than 1 183

5. The existence of Hadamard-type fractional derivatives and Hadamard-type differentiation and integration as reciprocal operations

186

(2)

References

188

(1)

Factorization of Singular Integral operators with a Carleman Shift via Factorization of Matrix Functions

by VIKTOR KRAVCHENKO, AMARINO LEBRE AND JUAN RODRÍGUEZ

1. Introduction

189

(3)

2. Preliminaries

192

(3)

3. Analysis of the case of a forward shift

195

(15)

References

210

(3)

Single Elements of Operator Algebras

by WILLIAM E. LONGSTAFF

1. Introduction

213

(1)

2. Results

214

(6)

References

220

(3)

Skew Incidence Half Plane Diffraction Problems: Particular Aspects of the Factorization Problem

by ERNST LUNEBURG AND HAMIT A. SERBEST

1. Introduction

223

(3)

2. Preliminaries

226

(4)

3. The two-face impedance half plane problem

230

(12)

4. Other examples

242

(5)

5. Concluding remarks

247

(1)

References

248

(5)

Aperiodic Wave Diffraction by a Half-Plane

by ERHARD MEISTER

1. Introduction

253

(1)

2. The field equations in elasto- and viscoelastodynamics

254

(1)

3. Initial boundary value problems

255

(5)

4. Conclusions

260

(1)

References

260

(3)

An Axiomatic Approach to the Limit Operators Method

by VLADIMIR S. RABINOVICH AND STEFFEN ROCH

1. Introduction

263

(1)

2. Abstract scheme for the method of limit operators

264

(5)

3. Fredholmness of convolution operators on homogeneous groups

269

(9)

4. Pseudodifferential operators

278

(6)

References

284

(3)

Algebras of Approximation Sequences: Structure of Fractal Algebras

by STEFFEN ROCH

1. Introduction

287

(4)

2. Fractality and Fredholmness of approximation sequences

291

(3)

3. Structure of certain fractal homomorphisms

294

(8)

4. The first half of the standard model

302

(2)

5. The second half of the standard model

304

(5)

References

309

(2)

Noncanonical Factorizations of Almost Periodic Multivariable Matrix Functions

by LEIBA RODMAN, ILYA M. SPITKOVSKY AND HUGO J. WOERDEMAN

1. Introduction

311

(2)

2. Definitions and preliminaries

313

(5)

3. Symmetric factorizations

318

(8)

4. Factorization and Toeplitz operators

326

(6)

5. Factorization indices under small perturbations; left vs right indices

332

(4)

6. Application of (non)canonical factorization to normalizing bases

336

(5)

References

341

(4)

Criterion for the Fredholmness of Singular Operators with Piecewise Continuous Coefficients in Generalized Hölder Spaces with Weight

by NATASHA SAMKO

1. Introduction

345

(1)

2. The results on Fredholmness

345

(4)

3. The proof of necessity

349

(6)

References

355

(2)

On Inversion of Fractional Spherical Potentials by Spherical Hypersingular Operators

by STEFAN SAMKO

1. Introduction

357

(1)

2. Preliminaries

357

(4)

3. Justification of the inversion in Lp(Sn-1) and identity approximation on the sphere

361

(4)

4. Inversion of the spherical Riesz potential in the case Ra > 2

365

(2)

References

367

(2)

An Axiomatic Approach to Stability of Approximation Sequences

by PEDRO A. SANTOS AND BERND SILBERMANN

1. Introduction

369

(2)

2. Algebraic results

371

(1)

3. Abstract Toeplitz operators

372

(1)

4. Approximation methods for the operator a(V), a E PC(T)

373

(6)

5. Finite subsection method for Toeplitz operators as example

379

(1)

References

380

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Singular Integral Operators, Factorization and Applications

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