Finite Sections Of Some Classical Inequalities

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Finite Sections Of Some Classical Inequalities

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Author : Herbert S. Wilf
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite Sections Of Some Classical Inequalities written by Herbert S. Wilf and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the restrictions approach the uniform bound. In the context of Toeplitz forms, such research was initiated over fifty years ago by Szego [37J, and the chain of ideas continues to grow strongly today, with fundamental contributions having been made by Kac, Widom, de Bruijn, and many others. In this monograph I attempt to draw together these lines of research from the point of view of sharpenings of the classical inequalities of [17]. This viewpoint leads to the exclusion of some material which might belong to a broader-based discussion, such as the elegant work of Baxter, Hirschman and others on the strong Szego limit theorem, and the inclusion of other work, such as that of de Bruijn and his students, which is basically nonlinear, and is therefore in some sense disjoint from the earlier investigations. I am grateful to Professor Halmos for inviting me to prepare this volume, and to Professors John and Olga Todd for several helpful comments. Philadelphia, Pa. H.S.W.

Finite Sections Of Seme Classical Inequalities

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Author : Herbert S. Wilf
language : en
Publisher:
Release Date : 1970

Finite Sections Of Seme Classical Inequalities written by Herbert S. Wilf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.

Factorizing The Classical Inequalities

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Author : Grahame Bennett
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Factorizing The Classical Inequalities written by Grahame Bennett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

This memoir describes a new way of looking at the classical inequalities. The most famous such results, (those of Hilbert, Hardy, and Copson) may be interpreted as inclusion relationships, l[superscript italic]p [subset equality symbol] [italic capital]Y, between certain (Banach) sequence spaces, the norm of the injection being the best constant of the particular inequality. The inequalities of Hilbert, Hardy, and Copson all share the same space [italic capital]Y. That space -- alias [italic]ces([italic]p) -- is central to many celebrated inequalities, and thus is studied here in considerable detail.

A Study Of Some Classical Inequalities And Their Generalizations

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Author :
language : en
Publisher:
Release Date : 2000

A Study Of Some Classical Inequalities And Their Generalizations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

Integral Operators In The Theory Of Linear Partial Differential Equations

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Author : Stefan Bergman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Integral Operators In The Theory Of Linear Partial Differential Equations written by Stefan Bergman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information.

Survey On Classical Inequalities

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Author : Themistocles RASSIAS
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Survey On Classical Inequalities written by Themistocles RASSIAS and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.

Catalog Of Copyright Entries Third Series

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Author : Library of Congress. Copyright Office
language : en
Publisher: Copyright Office, Library of Congress
Release Date : 1973

Catalog Of Copyright Entries Third Series written by Library of Congress. Copyright Office and has been published by Copyright Office, Library of Congress this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Copyright categories.

Indefinite Inner Product Spaces

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Author : J. Bognar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Indefinite Inner Product Spaces written by J. Bognar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja gin [1] gave the first mathematical treatment of an indefinite inner prod uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L. Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J.

A Survey Of Binary Systems

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Author : Richard Hubert Bruck
language : en
Publisher: Springer
Release Date : 2013-12-11

A Survey Of Binary Systems written by Richard Hubert Bruck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

Involutions On Manifolds

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Author : Santiago Lopez de Medrano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Involutions On Manifolds written by Santiago Lopez de Medrano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space.