Aspects of the Theory of Bounded Integral Operators in Lp-spaces PDF Download
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Author: George Olatokunbo Okikiolu
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 542
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Book Description
Author: George Olatokunbo Okikiolu
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 542
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Book Description
Author: P. R. Halmos
Publisher: Springer Science & Business Media
ISBN: 3642670164
Category : Mathematics
Languages : en
Pages : 147
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Book Description
The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.
Author: Paul Richard Halmos
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 160
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Book Description
Author: David E. Edmunds
Publisher: Springer Science & Business Media
ISBN: 940159922X
Category : Mathematics
Languages : en
Pages : 655
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Book Description
The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 234
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Book Description
Author: Michael Beals
Publisher: American Mathematical Soc.
ISBN: 0821822640
Category : Mathematics
Languages : en
Pages : 69
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Book Description
A class of Fourier integral operators is shown to be bounded on a range of [italic]L[superscript italic]p spaces depending on the order of the operator. The proof involves calculation of a partial asymptotic expansion for an oscillating integral. The results are applied to solutions of strongly hyperbolic partial differential equations.
Author: Vladimir I. Bogachev
Publisher: Springer Nature
ISBN: 3030382192
Category : Mathematics
Languages : en
Pages : 586
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Book Description
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
Author: Elliott H. Lieb
Publisher: Springer Science & Business Media
ISBN: 3642559255
Category : Mathematics
Languages : en
Pages : 687
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Book Description
Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.
Author: Paulus Gerdes
Publisher: Lulu.com
ISBN: 1430315377
Category : History
Languages : en
Pages : 432
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Book Description
This volume constitutes an updated version of the bibliography published in 2004 by the African Mathematical Union. The African Studies Association attributed the original edition a 'ÂÂspecial mention'ÂÂ in the 2006 Conover-Porter Award competition. The book contains over 1600 bibliographic entries. The appendices contain additional bibliographic information on (1) mathematicians of the Diaspora, (2) publications by Africans on the history of mathematics outside Africa, (3) time-reckoning and astronomy in African history and cultures, (4) string figures in Africa, (5) examples of books published by African mathematicians, (6) board games in Africa, (7) research inspired by geometric aspects of the 'ÂÂsona'ÂÂ tradition. The book concludes with several indices (subject, country, region, author, ethnographic and linguistic, journal, mathematicians). Professor Jan Persens of the University of the Western Cape (South Africa) and president of the African Mathematical Union (2000-2004) wrote the preface.
Author: Emmanuel Hebey
Publisher: Springer
ISBN: 3540699937
Category : Mathematics
Languages : en
Pages : 126
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Book Description
Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds. Hebey's presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be weakened, and also presents new results.
