Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 08 Aug 2020 07:06:13 GMT2020-08-08T07:06:13Z5021Vector interpretation of the matrix orthogonality on the real linehttp://hdl.handle.net/10316/13638Title: Vector interpretation of the matrix orthogonality on the real line
Authors: Branquinho, A.; Marcellán, F.; Mendes, A.
Abstract: In this paper we study sequences of vector orthogonal polynomials. The
vector orthogonality presented here provides a reinterpretation of what is known in
the literature as matrix orthogonality. These systems of orthogonal polynomials
satisfy three-term recurrence relations with matrix coefficients that do not obey
to any type of symmetry. In this sense the vectorial reinterpretation allows us to
study a non-symmetric case of the matrix orthogonality. We also prove that our
systems of polynomials are indeed orthonormal with respect to a complex measure
of orthogonality. Approximation problems of Hermite-Pad´e type are also discussed.
Finally, a Markov’s type theorem is presented.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136382009-01-01T00:00:00ZRelative asymptotics for orthogonal matrix polynomialshttp://hdl.handle.net/10316/13707Title: Relative asymptotics for orthogonal matrix polynomials
Authors: Branquinho, A.; Marcellán, F.; Mendes, A.
Abstract: 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.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137072010-01-01T00:00:00Z