A Discrete Hilbert Transform with Circle Packings, Volland

Автор: Young, N.
Название: An Introduction to hilbert spaces
ISBN: 0521337178 ISBN-13(EAN): 9780521337175
Издательство: Cambridge Academ
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Описание: This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained.

Автор: Yang Bicheng Et Al
Название: Half-Discrete Hilbert-Type Inequalities
ISBN: 9814504971 ISBN-13(EAN): 9789814504973
Издательство: World Scientific Publishing
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Описание: In 1934, G. H. Hardy et al. published a book entitled "Inequalities," in which a few theorems about Hilbert-type inequalities with homogeneous kernels of degree-one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof. Bicheng Yang in their four published books.This monograph deals with half-discrete Hilbert-type inequalities. By means of building the theory of discrete and integral Hilbert-type inequalities, and applying the technique of Real Analysis and Summation Theory, some kinds of half-discrete Hilbert-type inequalities with the general homogeneous kernels and non-homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed.The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.

Автор: P?ter G?bor Szab?; Mihaly Csaba Mark?t; Tibor Csen
Название: New Approaches to Circle Packing in a Square
ISBN: 0387456732 ISBN-13(EAN): 9780387456737
Издательство: Springer
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Описание: Summarizes results achieved in solving the circle packing problem. This work provides the reader with a comprehensive view of theoretical and computational achievements. It also includes a CD that provides the various open source programming codes used, enabling the reader to improve on them and solve the problem instances that remain challenging.