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Author : George Olatokunbo Okikiolu
Publisher : Unknown
Page : 542 pages
File Size : 49,6 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015015689493
Author : P. R. Halmos,V. S. Sunder
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642670169
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,V. S. Sunder
Publisher : Springer
Page : 160 pages
File Size : 54,5 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39015017294680
Author : Vladimir I. Bogachev,Oleg G. Smolyanov
Publisher : Springer Nature
Page : 586 pages
File Size : 40,5 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030382193
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
Page : 711 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642559259
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
Page : 432 pages
File Size : 48,7 Mb
Release : 2007
Category : History
ISBN : 9781430315377
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
Page : 126 pages
File Size : 46,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540699934
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 : Emmanuel Hebey
Publisher : American Mathematical Soc.
Page : 306 pages
File Size : 45,5 Mb
Release : 2000-10-27
Category : Mathematics
ISBN : 9780821827000
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 : S. P. Banks,A. J. Pritchard
Publisher : Elsevier
Page : 554 pages
File Size : 54,9 Mb
Release : 2014-05-18
Category : Computers
ISBN : 9781483151120
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,Ahmed Djebbar
Publisher : Lulu.com
Page : 450 pages
File Size : 40,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9781105141003
Author : Vladimir I. Bogachev
Publisher : Springer Science & Business Media
Page : 1075 pages
File Size : 45,7 Mb
Release : 2007-01-15
Category : Mathematics
ISBN : 9783540345145
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Author : N M Chuong,L Nirenberg,W Tutschke
Publisher : World Scientific
Page : 580 pages
File Size : 51,7 Mb
Release : 2004-06-01
Category : Mathematics
ISBN : 9789814482110
This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods. Topics include linear elliptic systems for composite material — the coefficients may jump from domain to domain; Stochastic Analysis — many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Deterministic Analysis:Differentiation of Hypergeometric Functions with Respect to Parameters (Yu A Brychkov & K O Geddes)On the Lagrange Problem About the Strongest Columns (Yu V Egorov)Wavelet Based Fast Solution of Boundary Integral Equations (H Harbrecht & R Schneider)Semi-Classical Methods in Ginzburg–Landau Theory (B Helffer)Stability of Equilibriums in One-Dimensional Motion of Compressible Viscous Gas Forced by Self-Gravity (Y Iwata & Y Yamamoto)Estimates for Elliptic Systems for Composite Material (L Nirenberg)On Asymptotics for the Mabuchi Energy Functional (D H Phong & J Sturm)Regularity of Solutions of the Initial Boundary Value Problem for Linearized Equations of Ideal Magneto-Hydrodynamics (M Yamamoto)Stochastic Analysis:Impulsive Stochastic Evolution Inclusions with Multi-Valued Diffusion (N U Ahmed)Some of Future Directions of White Noise Analysis (T Hida)Constructing Random Probability Distributions (T P Hill & D E R Sitton)Multiparameter Additive Processes of Mixture Type (K Inoue)The Random Integral Representation Hypothesis Revisited: New Classes of S-Selfdecomposable Laws (Z J Jurek)Semigroups and Processes with Parameter in a Cone (J Pedersen & K-I Sato)and other papers Readership: Researchers and academics in the fields of analysis and differential equations, approximation theory, probability and statistics. Keywords:Almost Complex Manifolds;Noncommutative Geometry;Lagrange Problem;Boundary Value Problem
Author : N. M. Chuong,L. Nirenberg,Wolfgang Tutschke
Publisher : World Scientific
Page : 579 pages
File Size : 53,7 Mb
Release : 2004
Category : History
ISBN : 9789812389442
This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material ? the coefficients may jump from domain to domain; Stochastic Analysis ? many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences
Author : Rudolf Hilfer
Publisher : World Scientific
Page : 473 pages
File Size : 40,6 Mb
Release : 2000-03-02
Category : Science
ISBN : 9789814496209
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.
Author : Wolfgang Walter
Publisher : Birkhäuser
Page : 507 pages
File Size : 50,9 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783034875653
The sixthInternational Conference on General Inequalities was held from Dec. 9 to Dec. 15, 1990, at the Mathematisches Forschungsinstitut Oberwolfach (Black Fa rest, Germany). The organizing committee was composed of W.N. Everitt (Birm ingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec ( Coimbra) served cheerfully and efficiently as secretary of the meeting. The con ference was attended by 44 participants from 20 countries. Yet again the importance of inequalities in both pure and applied mathematics was made evident from the wide range of interests of the individual participants, and from the wealth of new results announced. New inequalities were presented in the usual spread of the subject areas now expected for these meetings: Classical and functional analysis, existence and boundary value problems for both ordinary and partial differential equations, with special contributions to computer science, quantum holography and error analysis. More strongly than ever, the role played by modern electronic computers was made clear in testing out and prohing into the validity and structure of certain inequalities. Here the computer acts not only for numerical calculations of great complexity, but also in symbolic manipulation of complex finite structures. Prob lems in inequalities which even a few years ago were intractable, now fall to solution or receive direct and positive guidance as a result of computer applications. The interface between finite and infinite structures in mathematics and the versatility of modern computers is weil developed in the subject of general inequalities.
