Distributions and analytic functions

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 4
Preface......Page 7
Dedication......Page 11
1.1 Introduction and preliminaries......Page 12
1.2 The spaces D and D\'......Page 16
1.3 The spaces E and E\'......Page 26
1.4 The spaces S and S\'......Page 29
1.5 The spaces 0a and Oa......Page 34
1.6 The spaces DLp and D\'......Page 38
1.7 Convolution of distributions......Page 40
1.8 The Fourier transform......Page 46
1.9 The spaces Z and Z\'......Page 50
2.1 Introduction......Page 53
2.2 Distributional analytic continuation......Page 57
2.3 Analytic representation of distributions in E\' ([R)......Page 65
2.4 Analytic representation of distributions in O\' (IR )......Page 83
2.5 Distributional Plemelj relations and boundary value theorems......Page 94
2.6 Representation of half plane analytic and meromorphic functions......Page 100
2.7 Equivalence of convergence in DI(M) and 0a- (IR)......Page 114
2.8 Comments on Chapter 2......Page 117
3.1 Introduction......Page 122
3.2 Applications to boundary value problems......Page 127
3.3 Applications to singular convolution equations......Page 146
3.4 Comments on Chapter 3......Page 157
4.1 Introduction......Page 161
4.2 Analytic functions of several complex variables......Page 162
4.3 Cones in Rn and tubes in en......Page 164
4.4 Cauchy and Poisson kernel functions......Page 168
4.5 Hp functions in tubes......Page 178
4.6 Growth of Hp functions in tubes......Page 185
4.7 Fourier-Laplace transform of distributions and boundary values......Page 190
4.8 Comments on Chapter 4......Page 212
5.1 Introduction......Page 216
5.2 Analytic representation of distributions in E\': the scalar valued case......Page 217
5.3 Analytic representation of vector valued distributions of compact support......Page 233
5.4 Analytic representation of distributions in 0\'......Page 241
5.5 Analytic representation of distributions in D\'p......Page 243
5.6 Comments on Chapter 5......Page 269
6.1 Introduction......Page 271
6.2 The Cauchy integral of tempered distributions: the case corresponding to the quadrants in Rn......Page 273
6.3 Cauchy integral representation of the analytic functions which have S\' boundary values......Page 291
6.4 The Cauchy integral of tempered distributions: the case corresponding to arbitrary regular cones in Rn......Page 306
6.5 Analytic functions which have S\' boundary values and which are Hp functions......Page 312
6.6 Fourier-Laplace integral representation of  Hp functions......Page 332
6.7 Comments on Chapter 6......Page 338
References......Page 344
Index......Page 356