Methods of the Theory of Generalized FunctionsCRC Press, 15 ago 2002 - 328 pagine This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences. |
Sommario
Symbols and Definitions | 1 |
2 | 23 |
8 | 31 |
2 | 37 |
3 | 39 |
2 | 46 |
Integral Transformations of Generalized Functions | 50 |
10 | 61 |
Poisson Kernel and Poisson Transform | 152 |
Algebras of Holomorphic Functions | 159 |
Tauberian Theorems for Generalized Functions | 179 |
Some Applications in Mathematical Physics | 191 |
The Cauchy Problem | 213 |
Holomorphic Functions with Nonnegative Imaginary Part in TC | 229 |
5 Indicator of growth of functions of the class | 242 |
Holomorphic Functions with Nonnegative Imaginary Part in 7 | 249 |
12 | 73 |
6 | 96 |
25 | 104 |
Fourier Series of Periodic Generalized Functions | 113 |
4 | 119 |
3 | 125 |
The Laplace Transform of Tempered Generalized Functions | 126 |
The Cauchy Kernel and the Transforms of CauchyBochner | 133 |
Positive Real Matrix Functions in TC | 266 |
43 | 272 |
46 | 287 |
Abstract Scattering Operator | 295 |
303 | |
305 | |
309 | |
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