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:

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:

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.

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

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.

Download or read book Infinite Dimensional K hler 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.

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:

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.)

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.

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:

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.

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.

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

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.

Download or read book An Introduction to Infinite Dimensional Differential Geometry written by Alexander Schmeding and published by Cambridge University Press. This book was released on 2022-12-31 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, showcasing its modern applications.

Download or read book Infinite Dimensional K hler 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:

Download or read book Geometric and Algebraic Topological Methods in Quantum Mechanics written by G. Giachetta and published by World Scientific. This book was released on 2005 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.