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Constructive approximation by monogenic polynomials

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Resumo:In this thesis fundamentals of constructive approximation in Clifford Analysis are presented. This includes the consideration of Clifford algebravalued functions classes in different spaces related to special approximation problems. The problem of best approximation in Hilbert spaces of quaternionvalued functions is considered and the rate of convergence for the best approximation of a square-integrable function by general homogeneous monogenic polynomials is obtained. Furthermore, the construction of several complete systems of homogeneous monogenic polynomials is achieved using different methods. The first one is derived from the generalization of the complex powers by a permutational product. As an essential tool, the second method makes use of the hypercomplex derivative applied to a special system of real homogeneous harmonic polynomials. Moreover, orthogonality of the aforementioned systems, with respect to certain inner products, is investigated and complete orthonormal systems of homogeneous monogenic polynomials are constructed. A detailed analysis of these systems resulted in decompostion theorems of the considered function spaces. Some applications of the constructed systems, including the determination of monogenic primitives of monogenic functions, are presented.
Autores principais:Cação, Maria Isabel Jordão
Assunto:Matemática Análise de Clifford Aproximações (Matemática) Polinómios Espaços de Hilbert Funções monogénicas
Ano:2004
País:Portugal
Tipo de documento:tese de doutoramento
Tipo de acesso:acesso restrito
Instituição associada:Universidade de Aveiro
Idioma:inglês
Origem:RIA - Repositório Institucional da Universidade de Aveiro

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