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| Author(s): |
Vinicius Vieira Favaro
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2007-07-16 |
| Examining board members: |
Mário Carvalho de Matos;
Jorge Mujica;
Ary Orozimbo Chiacchio;
Antonio Roberto da Silva;
Daniel Marinho Pellegrino
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| Advisor: | Mário Carvalho de Matos |
| Abstract | |
In this work we introduce the spaces of (s; m (r , q))-summing functions of a given type and order defined in E, and the spaces of (s; (r, q))-quasi-nuclear functions of a given type and order defined in E, and we prove that the Fourier-Borel transform identify the dual of the space of (s; (r; q))-quasi-nuclear functions of a given type and order defined in E, with the space of (s' ; m (r'; q'))-summing functions of a corresponding type and order defined in E'. We also prove division theorems for (s; m (r; q))-summing functions of a given type and order and division theorems involving the Fourier-Borel transform. As a consequence we prove the existence and approximation results for convolution equations on the spaces of (s; (r; q))-quasi-nuclear functions of a given type and order (AU) | |