Detalhes do Documento

Relative asymptotics for orthogonal matrix polynomials

Autor(es): Branquinho, A. cv logo 1 ; Marcellán, F. cv logo 2 ; Mendes, A. cv logo 3

Data: 2010

Identificador Persistente: http://hdl.handle.net/10316/13707

Origem: Estudo Geral - Universidade de Coimbra

Assunto(s): Matrix orthogonal polynomials; Linear functional; Recurrence relation; Tridiagonal operator; Asymptotic results; Nevai class


Descrição
In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We study the generalized matrix Chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples. The concept of a Dirac delta functional is introduced. We show how the vector model that includes a Dirac delta functional is a representation of a discrete Sobolev inner product. It also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally, the relative asymptotics between a polynomial in the generalized matrix Nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a Dirac delta functional is deduced.
Tipo de Documento Preprint
Idioma Inglês
delicious logo  facebook logo  linkedin logo  twitter logo 
degois logo
mendeley logo

Documentos Relacionados



    Financiadores do RCAAP

Fundação para a Ciência e a Tecnologia Universidade do Minho   Governo Português Ministério da Educação e Ciência Programa Operacional da Sociedade do Conhecimento União Europeia