System Upgrade on Tue, May 28th, 2024 at 2am (EDT)
Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.For online purchase, please visit us again. Contact us at [email protected] for any enquiries.
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.
Sample Chapter(s)
Chapter 1: Cones in Rn and Kernels (169 KB)
Contents:
- Cones in Pn 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.
“This book contains a large amount of information on ultradistributions as boundary values of analytic functions, which will be useful for researchers on this topic and its applications to linear partial differential operators.”
Zentralblatt MATH
Sample Chapter(s)
Chapter 1: Cones in Rn and Kernels (169k)
