21,413 research outputs found
Boundary Conditions associated with the General Left-Definite Theory for Differential Operators
In the early 2000's, Littlejohn and Wellman developed a general left-definite
theory for certain self-adjoint operators by fully determining their domains
and spectral properties. The description of these domains do not feature
explicit boundary conditions. We present characterizations of these domains
given by the left-definite theory for all operators which possess a complete
system of orthogonal eigenfunctions, in terms of classical boundary conditions.Comment: 28 page
The Analytic Theory of Matrix Orthogonal Polynomials
We give a survey of the analytic theory of matrix orthogonal polynomials.Comment: 85 page
Semidefinite programming, harmonic analysis and coding theory
These lecture notes where presented as a course of the CIMPA summer school in
Manila, July 20-30, 2009, Semidefinite programming in algebraic combinatorics.
This version is an update June 2010
Multivariate Orthogonal Polynomials and Modified Moment Functionals
Multivariate orthogonal polynomials can be introduced by using a moment
functional defined on the linear space of polynomials in several variables with
real coefficients. We study the so-called Uvarov and Christoffel modifications
obtained by adding to the moment functional a finite set of mass points, or by
multiplying it times a polynomial of total degree 2, respectively. Orthogonal
polynomials associated with modified moment functionals will be studied, as
well as the impact of the modification in useful properties of the orthogonal
polynomials. Finally, some illustrative examples will be given
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