Semiclassical approximation addresses the important relationship between quantum and classical mechanics. In recent years mathematical theory has undergone significant growth, mainly due to microlocal analysis techniques. This volume develops the basic methods of the theory, inc…
Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB…
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB…
Properties of linear combinations of ridge functions -- The smoothness problem in ridge function representation -- Approximation of multivariate functions by sums of univariate functions -- Generalized ridge functions and linear superpositions -- Applications to neural networks.
"Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, an…
"Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, an…
In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions…
This book is devoted primarily to recent advances in applying the approximate analytical method of the separation of rapid and slow subsystems to other quantum realms. Such systems include hydrogen atoms in a high-frequency laser field, rotator-dipoles in a high-frequency field,…
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approx…
This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. With some few exceptions, a…