Series on Analysis, Applications and Computation - Vol. 1
BOUNDARY VALUES AND CONVOLUTION IN ULTRADISTRIBUTION SPACES
by Richard D Carmichael (Wake Forest University, USA), Andrzej Kamiński (University of Rzeszów, Poland) & Stevan Pilipović (University of Novi Sad, Serbia)
Table of Contents (89k)
Preface (118k)
Chapter 1: Cones in Rn and Kernels (169k)
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 ℝn and Kernels
- Ultradifferentiable
Functions and Ultradistributions
- Boundedness
- Cauchy and Poisson Integrals
- Boundary Values of Analytic Functions
- Convolution of Ultradistributions
- Integral Transforms of Tempered Ultradistributions
Readership: Researchers and graduate students in mathematics, especially
distributions and ultradistributions and their applications.
| 232pp |
Pub. date: Jul 2007 |
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