Integration On Infinite Dimensional Surfaces And Its Applications
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Integration On Infinite Dimensional Surfaces And Its Applications
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Author : A. Uglanov
language : en
Publisher:
Release Date : 2014-01-15
Integration On Infinite Dimensional Surfaces And Its Applications written by A. Uglanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Integration On Infinite Dimensional Surfaces And Its Applications
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Author : A. V. Uglanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-31
Integration On Infinite Dimensional Surfaces And Its Applications written by A. V. Uglanov 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 2000-01-31 with Mathematics categories.
This book presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fields, such as infinite dimensional distributions and differential equations (including boundary value problems), stochastic processes, approximation of functions, and calculus of variation on a Banach space, are treated in detail. Audience: This book will be of interest to specialists in functional analysis, and those whose work involves measure and integration, probability theory and stochastic processes, partial differential equations and mathematical physics.
Integration On Infinite Dimensional Surfaces And Its Applications
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Author : A. Uglanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Integration On Infinite Dimensional Surfaces And Its Applications written by A. Uglanov 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 2013-06-29 with Mathematics categories.
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.
Differentiable Measures And The Malliavin Calculus
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Author : Vladimir Igorevich Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-07-21
Differentiable Measures And The Malliavin Calculus written by Vladimir Igorevich Bogachev 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 2010-07-21 with Mathematics categories.
This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
High Dimensional Probability Iii
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Author : Joergen Hoffmann-Joergensen
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
High Dimensional Probability Iii written by Joergen Hoffmann-Joergensen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Lévy processes and Markov processes in general. The papers in this book reflect these broad categories. The volume thus will be a valuable resource for postgraduates and reseachers in probability theory and mathematical statistics.
Proceedings Of The International Conference On Stochastic Analysis And Applications
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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-07-28
Proceedings Of The International Conference On Stochastic Analysis And Applications written by Sergio Albeverio 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 2004-07-28 with Mathematics categories.
Stochastic analysis is a field of mathematical research having numerous interactions with other domains of mathematics such as partial differential equations, riemannian path spaces, dynamical systems, optimization. It also has many links with applications in engineering, finance, quantum physics, and other fields. This book covers recent and diverse aspects of stochastic and infinite-dimensional analysis. The included papers are written from a variety of standpoints (white noise analysis, Malliavin calculus, quantum stochastic calculus) by the contributors, and provide a broad coverage of the subject. This volume will be useful to graduate students and research mathematicians wishing to get acquainted with recent developments in the field of stochastic analysis.
Measure Theory
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Author : Vladimir I. Bogachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-15
Measure Theory written by Vladimir I. Bogachev 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 2007-01-15 with Mathematics categories.
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.
Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory
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Author : Palle Jorgensen
language : en
Publisher: World Scientific
Release Date : 2021-01-15
Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory written by Palle Jorgensen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-15 with Mathematics categories.
The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Infinite Dimensional Groups With Applications
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Author : Victor Kac
language : en
Publisher: Springer
Release Date : 2012-09-30
Infinite Dimensional Groups With Applications written by Victor Kac and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-30 with Mathematics categories.
This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.