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Author : George Olatokunbo Okikiolu
Publisher :
ISBN 13 :
Total Pages : 542 pages
Book Rating : 4.3/5 (91 download)
Download or read book Aspects of the Theory of Bounded Integral Operators in Lp-spaces written by George Olatokunbo Okikiolu and published by . This book was released on 1971 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. R. Halmos
Publisher : Springer Science & Business Media
ISBN 13 : 3642670164
Total Pages : 147 pages
Book Rating : 4.6/5 (426 download)
Download or read book Bounded Integral Operators on L 2 Spaces written by P. R. Halmos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : 160 pages
Book Rating : 4.3/5 (91 download)
Download or read book Bounded Integral Operators on L2 Spaces written by Paul Richard Halmos and published by Springer. This book was released on 1978 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David E. Edmunds
Publisher : Springer Science & Business Media
ISBN 13 : 940159922X
Total Pages : 655 pages
Book Rating : 4.4/5 (15 download)
Download or read book Bounded and Compact Integral Operators written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1975-12 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vakhtang Kokilashvili
Publisher : Birkhäuser
ISBN 13 : 3319210157
Total Pages : 567 pages
Book Rating : 4.3/5 (192 download)
Download or read book Integral Operators in Non-Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Author : Michael Beals
Publisher : American Mathematical Soc.
ISBN 13 : 0821822640
Total Pages : 69 pages
Book Rating : 4.8/5 (218 download)
Download or read book $L^p$ Boundedness of Fourier Integral Operators written by Michael Beals and published by American Mathematical Soc.. This book was released on 1982 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 3030382192
Total Pages : 586 pages
Book Rating : 4.0/5 (33 download)
Download or read book Real and Functional Analysis written by Vladimir I. Bogachev and published by Springer Nature. This book was released on 2020-02-25 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 3642559255
Total Pages : 687 pages
Book Rating : 4.6/5 (425 download)
Download or read book Inequalities written by Elliott H. Lieb and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 1430315377
Total Pages : 432 pages
Book Rating : 4.4/5 (33 download)
Download or read book Mathematics in African History and Cultures written by Paulus Gerdes and published by Lulu.com. This book was released on 2007 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 3540699937
Total Pages : 126 pages
Book Rating : 4.5/5 (46 download)
Download or read book Sobolev Spaces on Riemannian Manifolds written by Emmanuel Hebey and published by Springer. This book was released on 2006-11-14 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : R. M. Beals
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (17 download)
Download or read book Lp Boundedness of Fourier Integral Operators written by R. M. Beals and published by . This book was released on 1982 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Emmanuel Hebey
Publisher : American Mathematical Soc.
ISBN 13 : 0821827006
Total Pages : 306 pages
Book Rating : 4.8/5 (218 download)
Download or read book Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities written by Emmanuel Hebey and published by American Mathematical Soc.. This book was released on 2000-10-27 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. ``Several surprising phenomena appear when studying Sobolev spaces on manifolds,'' according to the author. ``Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role.'' The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces for compact manifolds. Chapter 3 presents the general theory of Sobolev spaces for complete, noncompact manifolds. Best constants problems for compact manifolds are discussed in Chapters 4 and 5. Chapter 6 presents special types of Sobolev inequalities under constraints. Best constants problems for complete noncompact manifolds are discussed in Chapter 7. Chapter 8 deals with Euclidean-type Sobolev inequalities. And Chapter 9 discusses the influence of symmetries on Sobolev embeddings. An appendix offers brief notes on the case of manifolds with boundaries. This topic is a field undergoing great development at this time. However, several important questions remain open. So a substantial part of the book is devoted to the concept of best constants, which appeared to be crucial for solving limiting cases of some classes of PDEs. The volume is highly self-contained. No familiarity is assumed with differentiable manifolds and Riemannian geometry, making the book accessible to a broad audience of readers, including graduate students and researchers.
Author : Viktor G. Kravchenko
Publisher : Springer Science & Business Media
ISBN 13 : 9401111804
Total Pages : 304 pages
Book Rating : 4.4/5 (11 download)
Download or read book Introduction to the Theory of Singular Integral Operators with Shift written by Viktor G. Kravchenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the Fredholm theory of singular integral operators with shift in Lp, 1
Author : S. P. Banks
Publisher : Elsevier
ISBN 13 : 1483151123
Total Pages : 554 pages
Book Rating : 4.4/5 (831 download)
Download or read book Control of Distributed Parameter Systems written by S. P. Banks and published by Elsevier. This book was released on 2014-05-18 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.
Author : Paulus Gerdes
Publisher : Lulu.com
ISBN 13 : 1105141004
Total Pages : 450 pages
Book Rating : 4.1/5 (51 download)
Download or read book History of Mathematics in Africa: 2000-2011 written by Paulus Gerdes and published by Lulu.com. This book was released on 2011 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ioseb Genebashvili
Publisher : CRC Press
ISBN 13 : 9780582302952
Total Pages : 432 pages
Book Rating : 4.3/5 (29 download)
Download or read book Weight Theory for Integral Transforms on Spaces of Homogeneous Type written by Ioseb Genebashvili and published by CRC Press. This book was released on 1997-05-15 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a space of homogeneous type, it continues with general criteria for the boundedness of the integral operators considered, then address special settings and applications to classical operators in Euclidean spaces.
