Integration on Infinite-Dimensional Surfaces and Its Applications

A. Uglanov

ISBN 10: 0792361334 / ISBN 13: 9780792361336

Published by Springer, 2000

About this Item

Integration on Infinite-Dimensional Surfaces and Its Applications | A. Uglanov | Buch | Einband - fest (Hardcover) | Englisch | 2000 | Springer | EAN 9780792361336 | Verantwortliche Person für die EU: Springer Netherlands, Haberstr. 7, 69126 Heidelberg, buchhandel-buch[at]springer[dot]com | Anbieter: preigu Print on Demand.

Seller Inventory # 102550114

Bibliographic Details

• Title: Integration on Infinite-Dimensional Surfaces and Its Applications
• Publisher: Springer
• Publication Date: 2000
• Language: English
• ISBN 10: 0792361334
• ISBN 13: 9780792361336
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 21D millimeters 241 millimeters width by 160 millimeters height by 21 millimeters depth
• Weight: 606 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

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.

Review

`This book is highly recommended for every mathematician with an interest in recent developments in functional analysis, measure and integration, differential equations, approximations, calculus of variations and stochastic processes.' Mathematical Reviews, 2001c