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Boundary values and convolution in ultradistribution spaces / Richard D. Carmichael, Andrzej Kamiński, Stevan Pilipović
Singapore : World Scientific, 2007.
xii, 217 pages. ; 24 cm.
Ký hiệu phân loại (DDC): 515.782
This book provides the construction and characterization of important ultradistribution spaces and studies properties and calculations of ultradistributions such as boundedness and convolution. Integral transforms of ultradistributions are constructed and analyzed. The general theory of the representation of ultradistributions as boundary values of analytic functions is obtained and the recovery of the analytic functions as Cauchy, Fourier-Laplace, and Poisson integrals associated with the boundary value is proved.
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Distribution theory : convolution, fourier transform, and laplace transform / Gerrit van Dijk.
Berlin : De Gruyter, 2013
118 pages. : illustrations ; 24 cm.
Ký hiệu phân loại (DDC): 515.723
The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensi
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