Undergraduate Thesis of Gonzalo Benavides
|Career||Mathematical Civil Engineering, Universidad de Concepción|
|Thesis Title||Orthogonal polynomials with reflection-invariant weights|
In this thesis we study multivariate orthogonal polynomials in the d-dimensional unit ball associated with a class of reflection-invariant weights, Wα,γ(x) := (1-||x||2)α Πi=1d |x_i|γ i , where α > -1 y γ = (γ 1,...,γ d) ∈ (-1,+∞)d. We obtain approximation properties of the related L2α,γ-orthogonal polynomial projector measured in what we call Dunkl—Sobolev norms, characterize a certain family of Sobolev-type orthogonal polynomials associated to the weight above, obtain connection relations of a specific bivariate basis to then develop computational tools to easily operate with polynomials expanded in terms of this basis.
|Thesis Director(s)||Leonardo Figueroa|
|Thesis Project Approval Date||2019, August 19|
|Thesis Defense Date||2020, March 27|
|PDF Tesis||Download Thesis PDF|