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Author : Mark Kac
Publisher :
ISBN 13 :
Total Pages : 98 pages
Book Rating : 4.3/5 (91 download)
Download or read book Integration in Function Spaces and Some of Its Applications written by Mark Kac and published by . This book was released on 1980 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Milan Kac
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (439 download)
Download or read book Integration in Function Spaces and Some of Its Applications written by Milan Kac and published by . This book was released on 1980 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. V. Skorohod
Publisher : Springer Science & Business Media
ISBN 13 : 3642656323
Total Pages : 192 pages
Book Rating : 4.6/5 (426 download)
Download or read book Integration in Hilbert Space written by A. V. Skorohod and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration in function spaces arose in probability theory when a gen eral theory of random processes was constructed. Here credit is cer tainly due to N. Wiener, who constructed a measure in function space, integrals-with respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe nomena. A. N. Kolmogorov generalized Wiener's construction to allow one to establish the existence of a measure corresponding to an arbitrary random process. These investigations were the beginning of the development of the theory of stochastic processes. A considerable part of this theory involves the solution of problems in the theory of measures on function spaces in the specific language of stochastic pro cesses. For example, finding the properties of sample functions is connected with the problem of the existence of a measure on some space; certain problems in statistics reduce to the calculation of the density of one measure w. r. t. another one, and the study of transformations of random processes leads to the study of transformations of function spaces with measure. One must note that the language of probability theory tends to obscure the results obtained in these areas for mathematicians working in other fields. Another dir,ection leading to the study of integrals in function space is the theory and application of differential equations. A. N.
Author : Michael Cwikel
Publisher :
ISBN 13 : 9783662192078
Total Pages : 456 pages
Book Rating : 4.1/5 (92 download)
Download or read book Function Spaces and Applications written by Michael Cwikel and published by . This book was released on 2014-01-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Uglanov
Publisher : Springer Science & Business Media
ISBN 13 : 9401596220
Total Pages : 280 pages
Book Rating : 4.4/5 (15 download)
Download or read book Integration on Infinite-Dimensional Surfaces and Its Applications written by A. Uglanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.
Author : Vakhtang Kokilashvili
Publisher : Birkhäuser
ISBN 13 : 3319210157
Total Pages : 585 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 585 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 : Hans Triebel
Publisher : Springer Science & Business Media
ISBN 13 : 3764375825
Total Pages : 433 pages
Book Rating : 4.7/5 (643 download)
Download or read book Theory of Function Spaces III written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.
Author : Luboš Pick
Publisher : Walter de Gruyter
ISBN 13 : 311025042X
Total Pages : 495 pages
Book Rating : 4.1/5 (12 download)
Download or read book Function Spaces, 1 written by Luboš Pick and published by Walter de Gruyter. This book was released on 2012-12-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.
Author : Mark Kac (Mathematiker, Polen, USA)
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (888 download)
Download or read book Integration in Function Spaces and Some of is Applications written by Mark Kac (Mathematiker, Polen, USA) and published by . This book was released on 1980 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Cwikel
Publisher : Springer
ISBN 13 :
Total Pages : 474 pages
Book Rating : 4.:/5 (318 download)
Download or read book Function Spaces and Applications written by Michael Cwikel and published by Springer. This book was released on 1988 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This seminar is a loose continuation of two previous conferences held in Lund (1982, 1983), mainly devoted to interpolation spaces, which resulted in the publication of the Lecture Notes in Mathematics Vol. 1070. This explains the bias towards that subject. The idea this time was, however, to bring together mathematicians also from other related areas of analysis. To emphasize the historical roots of the subject, the collection is preceded by a lecture on the life of Marcel Riesz.
Author : Dachun Yang
Publisher : Mdpi AG
ISBN 13 : 9783036540177
Total Pages : 408 pages
Book Rating : 4.5/5 (41 download)
Download or read book Recent Developments of Function Spaces and Their Applications I written by Dachun Yang and published by Mdpi AG. This book was released on 2022-05-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John-Nirenberg spaces, Sobolev spaces, and Besov and Triebel-Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation.
Author : Michel Willem
Publisher : Springer Science & Business Media
ISBN 13 : 1461470048
Total Pages : 220 pages
Book Rating : 4.4/5 (614 download)
Download or read book Functional Analysis written by Michel Willem and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis, in relation with integration and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics.
Author : K. Weber
Publisher : Routledge
ISBN 13 : 135143778X
Total Pages : 307 pages
Book Rating : 4.3/5 (514 download)
Download or read book Integration Theory written by K. Weber and published by Routledge. This book was released on 2020-04-28 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text acts as a singular resource for undergraduates learning the fundamental principles and applications of integration theory.Chapters discuss: function spaces and functionals, extension of Daniell spaces, measures of Hausdorff spaces, spaces of measures, elements of the theory of real functions on R.
Author : Miroslav Pavlović
Publisher : Walter de Gruyter
ISBN 13 : 3110281902
Total Pages : 463 pages
Book Rating : 4.1/5 (12 download)
Download or read book Function Classes on the Unit Disc written by Miroslav Pavlović and published by Walter de Gruyter. This book was released on 2013-12-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a study on various function classes, a number of new results and new or easy proofs of old results (Fefferman-Stein theorem on subharmonic behavior, theorems on conjugate functions and fractional integration on Bergman spaces, Fefferman's duality theorem), which are interesting for specialists; applications of the Hardy-Littlewood inequalities on Taylor coefficients to (C, α)-maximal theorems and (C, α)-convergence; a study of BMOA, due to Knese, based only on Green's formula; the problem of membership of singular inner functions in Besov and Hardy-Sobolev spaces; a full discussion of g-function (all p > 0) and Calderón's area theorem; a new proof, due to Astala and Koskela, of the Littlewood-Paley inequality for univalent functions; and new results and proofs on Lipschitz spaces, coefficient multipliers and duality, including compact multipliers and multipliers on spaces with non-normal weights. It also contains a discussion of analytic functions and lacunary series with values in quasi-Banach spaces with applications to function spaces and composition operators. Sixteen open questions are posed. The reader is assumed to have a good foundation in Lebesgue integration, complex analysis, functional analysis, and Fourier series. Further information can be found at the author's website at http://poincare.matf.bg.ac.rs/~pavlovic.
Author : A.D. Egorov
Publisher : Springer Science & Business Media
ISBN 13 : 9401117616
Total Pages : 421 pages
Book Rating : 4.4/5 (11 download)
Download or read book Functional Integrals written by A.D. Egorov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes. This monograph is devoted to numerical approximation methods of continual integration. A systematic description is given of the approximate computation methods of functional integrals on a wide class of measures, including measures generated by homogeneous random processes with independent increments and Gaussian processes. Many applications to problems which originate from analysis, probability and quantum physics are presented. This book will be of interest to mathematicians and physicists, including specialists in computational mathematics, functional and statistical physics, nuclear physics and quantum optics.
Author : Cécile Dewitt-Morette
Publisher : Springer Science & Business Media
ISBN 13 : 1489903194
Total Pages : 436 pages
Book Rating : 4.4/5 (899 download)
Download or read book Functional Integration written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.
Author : Jean-Pierre Antoine
Publisher : Springer Science & Business Media
ISBN 13 : 1461570352
Total Pages : 354 pages
Book Rating : 4.4/5 (615 download)
Download or read book Functional Integration written by Jean-Pierre Antoine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of the workshop on Functional Integration, Theory and Applications, held in Louvain-Ia-Neuve from November 6 to 9 1979, was to put in close and informal contact, during a few days, active workers in the field. There is no doubt now that functional integration is a tool that is being applied in all branches of modern physics. Since the earlier works of Dirac and Feynman enormous progress has been made, but unfortunately we lack still a unifying and rigo rous mathematical framework to account for all the situations in which one is interested. We are then in presence of a rapid ly changing field in which new achievements, proposals, and points of view are the normal pattern. Considering this state of affairs we have decided to order the articles starting from the more fundamental and ambitious from the point of view of mathematical rigour, followed by ar ticles in which the main interest is the application to con crete physical situations. It is obvious that this ordering should not be taken too seriously since in many cases there will be an interplay of both objects.
