Integration on Infinite-Dimensional Surfaces and Its Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Mathematics and Its Applications
496 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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. |
| Beschreibung: | 1 Online-Ressource (IX, 272 p) |
| ISBN: | 9789401596220 9789048153848 |
| DOI: | 10.1007/978-94-015-9622-0 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424157 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2000 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401596220 |c Online |9 978-94-015-9622-0 | ||
| 020 | |a 9789048153848 |c Print |9 978-90-481-5384-8 | ||
| 024 | 7 | |a 10.1007/978-94-015-9622-0 |2 doi | |
| 035 | |a (OCoLC)864102260 | ||
| 035 | |a (DE-599)BVBBV042424157 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.42 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Uglanov, A. V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integration on Infinite-Dimensional Surfaces and Its Applications |c by A. V. Uglanov |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2000 | |
| 300 | |a 1 Online-Ressource (IX, 272 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications |v 496 | |
| 500 | |a 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. | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Measure and Integration | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Theoretical, Mathematical and Computational Physics | |
| 650 | 4 | |a Mathematik | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-015-9622-0 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859574 | ||
Datensatz im Suchindex
| _version_ | 1804153100757368832 |
|---|---|
| any_adam_object | |
| author | Uglanov, A. V. |
| author_facet | Uglanov, A. V. |
| author_role | aut |
| author_sort | Uglanov, A. V. |
| author_variant | a v u av avu |
| building | Verbundindex |
| bvnumber | BV042424157 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864102260 (DE-599)BVBBV042424157 |
| dewey-full | 515.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 |
| dewey-search | 515.42 |
| dewey-sort | 3515.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9622-0 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03040nmm a2200481zcb4500</leader><controlfield tag="001">BV042424157</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2000 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401596220</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-015-9622-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048153848</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-5384-8</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-015-9622-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)864102260</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424157</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.42</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Uglanov, A. V.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integration on Infinite-Dimensional Surfaces and Its Applications</subfield><subfield code="c">by A. V. Uglanov</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">2000</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (IX, 272 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">496</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, partial</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Measure and Integration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probability Theory and Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Partial Differential Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Theoretical, Mathematical and Computational Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-015-9622-0</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859574</subfield></datafield></record></collection> |
| id | DE-604.BV042424157 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401596220 9789048153848 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859574 |
| oclc_num | 864102260 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (IX, 272 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| 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 |