Kernel-Based Approximation Methods Using Matlab, Fasshauer Gregory E Et Al

Автор: Anastassiou George A
Название: Frontiers In Approximation Theory
ISBN: 9814696080 ISBN-13(EAN): 9789814696081
Издательство: World Scientific Publishing
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Описание:

This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.

The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.

The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.

Автор: Jay Jorgenson; Serge Lang
Название: The Heat Kernel and Theta Inversion on SL2(C)
ISBN: 1441922822 ISBN-13(EAN): 9781441922823
Издательство: Springer
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Описание: The purpose of this text is to provide a self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, this one begins with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion.