Integration on Infinite-Dimensional Surfaces and Its Applications (Mathematics and Its Applications, 496)
ISBN-13:
9789048153848
ISBN-10:
9048153840
Edition:
Softcover reprint of hardcover 1st ed. 2000
Author:
A. Uglanov
Publication date:
2010
Publisher:
Springer
Format:
Paperback
281 pages
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Book details
ISBN-13:
9789048153848
ISBN-10:
9048153840
Edition:
Softcover reprint of hardcover 1st ed. 2000
Author:
A. Uglanov
Publication date:
2010
Publisher:
Springer
Format:
Paperback
281 pages
Summary
Integration on Infinite-Dimensional Surfaces and Its Applications (Mathematics and Its Applications, 496) (ISBN-13: 9789048153848 and ISBN-10: 9048153840), written by authors
A. Uglanov, was published by Springer in 2010.
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Description
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.
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