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Integration on Infinite-Dimensional Surfaces and Its Applications
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Catalogue Information
Field name
Details
Dewey Class
515.42
Title
Integration on Infinite-Dimensional Surfaces and Its Applications ([EBook]) / by A. V. Uglanov.
Author
Uglanov, Aleksej V.
Other name(s)
SpringerLink (Online service)
Publication
Dordrecht : Springer Netherlands , 2000.
Physical Details
IX, 272 pages : online resource.
Series
Mathematics and its applications
; 496
ISBN
9789401596220
Summary Note
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.:
Contents note
Basic Notations -- 1. Vector Measures and Integrals -- 2. Surface Integrals -- 3. Applications -- Comments -- References.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-94-015-9622-0
Links to Related Works
Subject References:
Functional Analysis
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Manifolds (Mathematics)
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Measure and Integration
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Measure theory
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Partial differential equations
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Probabilities
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Theoretical, Mathematical and Computational Physics
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Authors:
Uglanov, Aleksej V.
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Uglanov, Aleksej V.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Mathematics and its applications
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Classification:
515.42
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