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Author : Hui-hsiung Kuo
Publisher :
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.E/5 ( download)
Download or read book Integration Theory on Infinite Dimensional Manifolds written by Hui-hsiung Kuo and published by . This book was released on 1970 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Roald Ramer
Publisher :
ISBN 13 :
Total Pages : 155 pages
Book Rating : 4.:/5 (69 download)
Download or read book Integration on infinite dimensional manifolds written by Roald Ramer and published by . This book was released on 1974 with total page 155 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 :
Publisher : Academic Press
ISBN 13 : 0080873634
Total Pages : 439 pages
Book Rating : 4.0/5 (88 download)
Download or read book Measure and Integration Theory on Infinite-Dimensional Spaces written by and published by Academic Press. This book was released on 1972-10-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure and Integration Theory on Infinite-Dimensional Spaces
Author : Katsuro Sakai
Publisher : Springer Nature
ISBN 13 : 9811575754
Total Pages : 619 pages
Book Rating : 4.8/5 (115 download)
Download or read book Topology of Infinite-Dimensional Manifolds written by Katsuro Sakai and published by Springer Nature. This book was released on 2020-11-21 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk’s conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial ∞-manifolds, the infinite-dimensional version of combinatorial n-manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial ∞-manifold and the Hauptvermutung for them is true.
Author : Alan Huckleberry
Publisher : Birkhäuser
ISBN 13 : 3034882270
Total Pages : 385 pages
Book Rating : 4.0/5 (348 download)
Download or read book Infinite Dimensional Kähler Manifolds written by Alan Huckleberry and published by Birkhäuser. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.
Author : James Joseph Callahan
Publisher :
ISBN 13 :
Total Pages : 98 pages
Book Rating : 4.:/5 (394 download)
Download or read book Intersection Theory for Infinite-dimensional Manifolds written by James Joseph Callahan and published by . This book was released on 1967 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H Kunita
Publisher : CRC Press
ISBN 13 : 9780582244900
Total Pages : 340 pages
Book Rating : 4.2/5 (449 download)
Download or read book Stochastic Analysis on Infinite Dimensional Spaces written by H Kunita and published by CRC Press. This book was released on 1994-08-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the following topics in stochastic analysis: 1. Stochastic analysis related to Lie groups: stochastic analysis of loop spaces and infinite dimensional manifolds has been developed rapidly after the fundamental works of Gross and Malliavin. (Lectures by Driver, Gross, Mitoma, and Sengupta.)
Author : Hui-Hsiung Kuo
Publisher : American Mathematical Soc.
ISBN 13 : 0821832026
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)
Download or read book Finite and Infinite Dimensional Analysis in Honor of Leonard Gross written by Hui-Hsiung Kuo and published by American Mathematical Soc.. This book was released on 2003 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross's former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross's work and permeate diverse fields. Topics include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.
Author : Robert Geroch
Publisher : Minkowski Institute Press
ISBN 13 : 1927763169
Total Pages : 137 pages
Book Rating : 4.9/5 (277 download)
Download or read book Infinite-Dimensional Manifolds written by Robert Geroch and published by Minkowski Institute Press. This book was released on 2013-12-16 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert Geroch's lecture notes "Infinite-Dimensional Manifolds" provide a concise, clear, and helpful introduction to a wide range of subjects, which are essential in mathematical and theoretical physics - Banach spaces, open mapping theorem, splitting, bounded linear mappings, derivatives, mean value theorem, manifolds, mappings of manifolds, scalar and vector fields, tensor products, tensor spaces, natural tensors, tensor fields, tensor bundles, Lie derivatives, integral curves, geometry of Lie derivatives, exterior derivatives, derivative operators, partial differential equations, and Riemannian geometry. Like in his other books, Geroch explains even the most abstract concepts with the help of intuitive examples and many (over 60) figures. Like Geroch's other books, this book too can be used for self-study since each chapter contains examples plus a set of problems given in the Appendix.
Author : T. A. Chapman
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (897 download)
Download or read book On Some Applications of Infinite- Dimensional Manifolds to the Theory of Shape written by T. A. Chapman and published by . This book was released on 1971 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ana Isabel Cardoso
Publisher : Springer Science & Business Media
ISBN 13 : 9401102198
Total Pages : 455 pages
Book Rating : 4.4/5 (11 download)
Download or read book Stochastic Analysis and Applications in Physics written by Ana Isabel Cardoso and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993
Author : Andreas Kriegl
Publisher : American Mathematical Soc.
ISBN 13 : 0821807803
Total Pages : 631 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Convenient Setting of Global Analysis written by Andreas Kriegl and published by American Mathematical Soc.. This book was released on 1997 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR
Author : T. Voronov
Publisher : CRC Press
ISBN 13 : 9783718651993
Total Pages : 152 pages
Book Rating : 4.6/5 (519 download)
Download or read book Geometric Integration Theory on Supermanifolds written by T. Voronov and published by CRC Press. This book was released on 1991 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author presents the first detailed and original account of his theory of forms on supermanifolds-a correct and non-trivial analogue of Cartan-de Rham theory based on new concepts. The paper develops the apparatus of supermanifold differential topology necessary for the integration theory. A key feature is the identification of a class of proper morphisms intimately connected with Berezin integration, which are of fundamental importance in various problems. The work also contains a condensed introduction to superanalysis and supermanifolds, free from algebraic formalism, which sets out afresh such challenging problems as the Berezin intgegral on a bounded domain.
Author : Alan T. Huckleberry
Publisher : Birkhauser
ISBN 13 : 9780817666026
Total Pages : 375 pages
Book Rating : 4.6/5 (66 download)
Download or read book Infinite Dimensional Kähler Manifolds written by Alan T. Huckleberry and published by Birkhauser. This book was released on 2001-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sergio Albeverio
Publisher : Springer Science & Business Media
ISBN 13 : 940117976X
Total Pages : 254 pages
Book Rating : 4.4/5 (11 download)
Download or read book Stochastics, Algebra and Analysis in Classical and Quantum Dynamics written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, "'f si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile':' human race. It has put common sense back Jules Verne where it belongs, 011 the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . . . '; 'One service logic has rendered com puter science . . . '; 'One service category theory has rendered mathematics . . . '. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its Applications, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote ''Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.
Author : Richard S. Palais
Publisher :
ISBN 13 :
Total Pages : 386 pages
Book Rating : 4.3/5 (91 download)
Download or read book Lectures on the Differential Topology of Infinite Dimensional Manifolds written by Richard S. Palais and published by . This book was released on 1966 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
