Boundary Values and Convolution in Ultradistribution Spaces (Series on Analysis, Applications and Computation)

Pilipovic, Stevan/ Carmichael, Richard D/ Kaminski, Andrzej

World Scientific Publishing Co Pte Ltd（2007/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 232 p.
• 言語 ENG
• 商品コード 9789812707697
• DDC分類 515.35

Full Description

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.Ultradistributions are useful in applications in quantum field theory, partial differential equations, convolution equations, harmonic analysis, pseudo-differential theory, time-frequency analysis, and other areas of analysis. Thus this book is of interest to users of ultradistributions in applications as well as to research mathematicians in areas of analysis.

Contents

Cones in n and Kernels; Ultradifferentiable Functions and Ultradistributions; Boundedness; Cauchy and Poisson Integrals; Boundary Values of Analytic Functions; Convolution of Ultradistributions; Integral Transforms of Tempered Ultradistributions.