Integration on Infinite-Dimensional Surfaces and Its Applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2000
|
| Series: | Mathematics and Its Applications
496 |
| Subjects: | |
| Online Access: | Volltext |
| Item 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. |
| Physical Description: | 1 Online-Ressource (IX, 272 p) |
| ISBN: | 9789401596220 9789048153848 |
| DOI: | 10.1007/978-94-015-9622-0 |
Staff View
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| id | DE-604.BV042424157 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401596220 9789048153848 |
| language | English |
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| physical | 1 Online-Ressource (IX, 272 p) |
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| spelling | Uglanov, A. V. Verfasser aut Integration on Infinite-Dimensional Surfaces and Its Applications by A. V. Uglanov Dordrecht Springer Netherlands 2000 1 Online-Ressource (IX, 272 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 496 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. Mathematics Functional analysis Differential equations, partial Distribution (Probability theory) Measure and Integration Functional Analysis Probability Theory and Stochastic Processes Partial Differential Equations Theoretical, Mathematical and Computational Physics Mathematik https://doi.org/10.1007/978-94-015-9622-0 Verlag Volltext |
| spellingShingle | Uglanov, A. V. Integration on Infinite-Dimensional Surfaces and Its Applications Mathematics Functional analysis Differential equations, partial Distribution (Probability theory) Measure and Integration Functional Analysis Probability Theory and Stochastic Processes Partial Differential Equations Theoretical, Mathematical and Computational Physics Mathematik |
| title | Integration on Infinite-Dimensional Surfaces and Its Applications |
| title_auth | Integration on Infinite-Dimensional Surfaces and Its Applications |
| title_exact_search | Integration on Infinite-Dimensional Surfaces and Its Applications |
| title_full | Integration on Infinite-Dimensional Surfaces and Its Applications by A. V. Uglanov |
| title_fullStr | Integration on Infinite-Dimensional Surfaces and Its Applications by A. V. Uglanov |
| title_full_unstemmed | Integration on Infinite-Dimensional Surfaces and Its Applications by A. V. Uglanov |
| title_short | Integration on Infinite-Dimensional Surfaces and Its Applications |
| title_sort | integration on infinite dimensional surfaces and its applications |
| topic | Mathematics Functional analysis Differential equations, partial Distribution (Probability theory) Measure and Integration Functional Analysis Probability Theory and Stochastic Processes Partial Differential Equations Theoretical, Mathematical and Computational Physics Mathematik |
| topic_facet | Mathematics Functional analysis Differential equations, partial Distribution (Probability theory) Measure and Integration Functional Analysis Probability Theory and Stochastic Processes Partial Differential Equations Theoretical, Mathematical and Computational Physics Mathematik |
| url | https://doi.org/10.1007/978-94-015-9622-0 |
| work_keys_str_mv | AT uglanovav integrationoninfinitedimensionalsurfacesanditsapplications |