Description

Book Synopsis
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.

Table of 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.

Boundary Values And Convolution In

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    A Hardback by Stevan Pilipovic, Richard D Carmichael, Andrzej Kaminski

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 31 July 2007
      ISBN-13 9789812707697
      978-9812707697
      ISBN-10 9812707697

      Description

      Book Synopsis
      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.

      Table of 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.

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