Harmonic Analysis in Hypercomplex Systems

Harmonic Analysis in Hypercomplex Systems
Author :
Publisher : Springer Science & Business Media
Total Pages : 494
Release :
ISBN-10 : 9789401717588
ISBN-13 : 9401717583
Rating : 4/5 (583 Downloads)

Book Synopsis Harmonic Analysis in Hypercomplex Systems by : Yu.M. Berezansky

Download or read book Harmonic Analysis in Hypercomplex Systems written by Yu.M. Berezansky and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the "basis" of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples.


Harmonic Analysis in Hypercomplex Systems Related Books

Harmonic Analysis in Hypercomplex Systems
Language: en
Pages: 494
Authors: Yu.M. Berezansky
Categories: Mathematics
Type: BOOK - Published: 2013-06-29 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operato
Harmonic Analysis of Probability Measures on Hypergroups
Language: en
Pages: 609
Authors: Walter R. Bloom
Categories: Mathematics
Type: BOOK - Published: 2011-04-20 - Publisher: Walter de Gruyter

DOWNLOAD EBOOK

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering
Modern Methods in Operator Theory and Harmonic Analysis
Language: en
Pages: 474
Authors: Alexey Karapetyants
Categories: Mathematics
Type: BOOK - Published: 2019-08-28 - Publisher: Springer Nature

DOWNLOAD EBOOK

This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII
Applications of Hypergroups and Related Measure Algebras
Language: en
Pages: 458
Authors:
Categories: Mathematics
Type: BOOK - Published: 1995-02-28 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

`The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergrou
Generalized Harmonic Analysis and Wavelet Packets
Language: en
Pages: 319
Authors: Khalifa Trimeche
Categories: Mathematics
Type: BOOK - Published: 2001-03-07 - Publisher: CRC Press

DOWNLOAD EBOOK

The book presents a more comprehensive treatment of transmutation operators associated with the Bessel operator, and explores many of their properties. They are