Boundary values and convolution in ultradistribution spaces

Richard D. Carmichael, Andrzej Kaminski, Stevan Pilipovic9812707697, 9789812707697

Advances in Geosciences is the result of a concerted effort in bringing the latest results and planning activities related to earth and space science in Asia and the international arena. The volume editors are all leading scientists in their research fields covering six sections: Hydrological Science (HS), Planetary Science (PS), Solar Terrestrial (ST), Solid Earth (SE), Ocean Science (OS) and Atmospheric Science (AS). The main purpose is to highlight the scientific issues essential to the study of earthquakes, tsunamis, atmospheric dust storms, climate change, drought, flood, typhoons, monsoons, space weather, and planetary exploration.

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Table of contents :
Contents……Page 12
Preface……Page 6
1.1 Notation……Page 14
1.2 Cones in Rn……Page 17
1.3 Cauchy and Poisson kernels……Page 20
2.1 Sequences (Mp)……Page 26
2.2 Ultradi erential operators……Page 30
2.3 Functions and ultradistributions of Beurling and Roumieu type……Page 33
2.4 Fourier transform on D( .Ls) and D0( ,Ls)……Page 39
2.5 Ultradi erentiable functions of ultrapolynomial growth……Page 41
2.6 Tempered ultradistributions……Page 50
2.7 Laplace transform……Page 53
3.1 Boundedness in 0( ;Ls)……Page 54
3.2 Boundedness in S……Page 60
4.1 Cauchy and Poisson kernels as ultradifferentiable functions……Page 64
4.2 Cauchy integral of ultradistributions……Page 74
4.3 Poisson integral of ultradistributions……Page 89
5.1 Generalizations of Hr functions in tubes……Page 94
5.2 Boundary values in D0((Mp);Ls) for analytic functions in tubes……Page 104
5.3 Case 2 < r < 1……Page 124
5.4 Boundary values via almost analytic extensions……Page 131
5.5 Cases s = 1 and s = 1……Page 142
6.1 Introduction……Page 148
6.2 Definitions of 0(Mp) convolution……Page 150
6.3 Equivalence of definitions of 0(Mp) convolution……Page 153
6.4 Definitions of 0(Mp) convolution……Page 160
6.5 Equivalence of difinitions of S(mp) – convolution……Page 163
6.6 Existence of D0(Mp) – and S (Mp) – convolution……Page 166
6.7 Compatibility conditions on supports……Page 170
6.8 Convolution in weighted spaces……Page 175
7.1 Introductory remarks……Page 186
7.2 Definitions……Page 187
7.3 Characterizations of some integral transforms……Page 192
7.4 Laplace transform……Page 193
7.5 Proof of equivalence of families of norms……Page 195
7.6 Hilbert transform……Page 199
7.6.1 One-dimensional case……Page 200
7.6.2 Multi-dimensional case……Page 209
7.7 Singular integral operators……Page 212
Bibliography……Page 218
Index……Page 226