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Presents the theory of elliptic functions and its applications. Suitable primarily for engineers who work with elliptic functions, this work is also intended for those with background in the elements of mathematical analysis and the theory of functions contained in the first two years of mathematics and physics courses at the college level.
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of problems and applications (elementary extremal problems, Szego's theorem, the Carathéodory-Fejér problem, and more).
Presents, at a level suitable for undergraduates and technical college students, the basic physical theory of mechanics and the molecular structure of matter. The material contained in the work should correspond quite closely to courses of lectures given to undergraduate students of physics in Britain and America.
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Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity i...
This book considers the theory of 'integrable' non-linear partial differential equations. The theory was developed at first by mathematical physicists but later mathematicians, particularly from the Soviet Union, were attracted to the field. In this volume are reprinted some fundamental contributions, originally published in Russian Mathematical Surveys, from some of the leading Soviet workers. Dr George Wilson has written an introduction intended to smooth the reader's path through some of the articles.
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The main topic of this book is the sudy of the interaction between two major subjects of modern mathematics, namely, the theory of Lie groups with its specific methods and ways of thinking on the one hand and complex analysis with all its analytic, algebraic and geometric aspects. More specifically, the author concentrates on the double role of Lie groups in complex analysis, namely, as groups of biholomorphic self-made of certain complex analytic objects on the one hand and as a special class of complex manifolds with an additional strong structure on the other hand. The book starts from the basics of this subject and introduces the reader into many fields of recent research.