Sobolev orthogonality of polynomial solutions of second-order partial differential equations

dc.contributor.authorGarcía-Ardila, Juan Carlos
dc.contributor.authorMarriaga, Misael E.
dc.date.accessioned2023-01-13T14:37:40Z
dc.date.available2023-01-13T14:37:40Z
dc.date.issued2022-12-16
dc.description.abstractGiven a second-order partial differential operator L with nonzero polynomial coefficients of degree at most 2, and a Sobolev bilinear form (P,Q)S=∑i=0N∑j=0i⟨u(i,j),(∂^(i−j)_x∂^j_yP∂^(i−j)_x∂^j_yQ⟩,N⩾0, where u(i,j), 0⩽j⩽i⩽N, are linear functionals defined on the space of bivariate polynomials, we study the orthogonality of the polynomial solutions of the partial differential equation L[p]=λn,mp with respect to (⋅,⋅)S, where λn,m are eigenvalue parameters depending on the total and partial degree of the solutions. We show that the linear functionals in the bilinear form must satisfy Pearson equations related to the coefficients of L. Therefore, we also study solutions of the Pearson equations that can be obtained from univariate moment functionals. In fact, the involved univariate functionals must satisfy Pearson equations in one variable. Moreover, we study polynomial solutions of L[p]=λn,mp obtained from univariate sequences of polynomials satisfying second-order ordinary differential equations.es
dc.identifier.citationGarcía-Ardila, J.C., Marriaga, M.E. Sobolev orthogonality of polynomial solutions of second-order partial differential equations. Comp. Appl. Math. 42, 13 (2023).es
dc.identifier.doi10.1007/s40314-022-02152-2es
dc.identifier.urihttps://hdl.handle.net/10115/20922
dc.language.isoenges
dc.publisherSpringeres
dc.rights.accessRightsinfo:eu-repo/semantics/embargoedAccesses
dc.subjectBivariate orthogonal polynomials, Sobolev orthogonal polynomialses
dc.titleSobolev orthogonality of polynomial solutions of second-order partial differential equationses
dc.typeinfo:eu-repo/semantics/articlees

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