Publicação
On normal families and growth behavior of polymonogenic functions
| Resumo: | The aim of this work is to provide some contributions to the study of normal family of special meromorphic functions as well as to the study of the asymptotic behaviour of polymonogenic functions in the framework of Hypercomplex Analysis. In this context we have obtained necessary and/or sufficient normality conditions for families of special meromorphic functions, in particular, a generalization of Marty’s criterion and also of Zalcman’s lemma. We prove inequalities of Cauchy-type estimates for a class of polymonogenic functions and also some generalizations of results of the Wiman-Valiron theory. Consequently, relations of the maximum modulus, the maximum term and the norm of the central index with respect to their Taylor-Almansi series expansion are obtained. These results are applied to the asymptotic growth behaviour of those functions classes. As applications we establish theorems on the asymptotic of solutions of certain partial differential equations which allow us to provide a classification of some of such solutions. |
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| Autores principais: | Almeida, Regina de |
| Assunto: | Matemática Análise de Clifford Funções polimonogénicas |
| Ano: | 2006 |
| País: | Portugal |
| Tipo de documento: | tese de doutoramento |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Aveiro |
| Idioma: | português |
| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
| Resumo: | The aim of this work is to provide some contributions to the study of normal family of special meromorphic functions as well as to the study of the asymptotic behaviour of polymonogenic functions in the framework of Hypercomplex Analysis. In this context we have obtained necessary and/or sufficient normality conditions for families of special meromorphic functions, in particular, a generalization of Marty’s criterion and also of Zalcman’s lemma. We prove inequalities of Cauchy-type estimates for a class of polymonogenic functions and also some generalizations of results of the Wiman-Valiron theory. Consequently, relations of the maximum modulus, the maximum term and the norm of the central index with respect to their Taylor-Almansi series expansion are obtained. These results are applied to the asymptotic growth behaviour of those functions classes. As applications we establish theorems on the asymptotic of solutions of certain partial differential equations which allow us to provide a classification of some of such solutions. |
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