Differentiation Theory over Infinite-Dimensional Banach Spaces
We study, for any positive integer k and for any subset I of N⁎, the Banach space EI of the bounded real sequences xnn∈I and a measure over RI,B(I) that generalizes the k-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/2619087 |
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| author | Claudio Asci |
| author_facet | Claudio Asci |
| author_sort | Claudio Asci |
| collection | DOAJ |
| description | We study, for any positive integer k and for any subset I of N⁎, the Banach space EI of the bounded real sequences xnn∈I and a measure over RI,B(I) that generalizes the k-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables’ formula for the integration of the measurable real functions on RI,B(I). This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms. |
| format | Article |
| id | doaj-art-473e147109b64b81aee396adc1d68c08 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-473e147109b64b81aee396adc1d68c082025-02-03T01:27:09ZengWileyJournal of Mathematics2314-46292314-47852016-01-01201610.1155/2016/26190872619087Differentiation Theory over Infinite-Dimensional Banach SpacesClaudio Asci0Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Via Valerio 12/1, 34127 Trieste, ItalyWe study, for any positive integer k and for any subset I of N⁎, the Banach space EI of the bounded real sequences xnn∈I and a measure over RI,B(I) that generalizes the k-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables’ formula for the integration of the measurable real functions on RI,B(I). This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms.http://dx.doi.org/10.1155/2016/2619087 |
| spellingShingle | Claudio Asci Differentiation Theory over Infinite-Dimensional Banach Spaces Journal of Mathematics |
| title | Differentiation Theory over Infinite-Dimensional Banach Spaces |
| title_full | Differentiation Theory over Infinite-Dimensional Banach Spaces |
| title_fullStr | Differentiation Theory over Infinite-Dimensional Banach Spaces |
| title_full_unstemmed | Differentiation Theory over Infinite-Dimensional Banach Spaces |
| title_short | Differentiation Theory over Infinite-Dimensional Banach Spaces |
| title_sort | differentiation theory over infinite dimensional banach spaces |
| url | http://dx.doi.org/10.1155/2016/2619087 |
| work_keys_str_mv | AT claudioasci differentiationtheoryoverinfinitedimensionalbanachspaces |