Person: Gómez-Ullate Oteiza, David
Universidad Complutense de Madrid
Faculty / Institute
Now showing 1 - 4 of 4
PublicationExceptional Legendre polynomials and confluent Darboux transformations(Natl Acad Sci Ukraine, Inst Math, 2021) Garcia Ferrero, María Ángeles; Gómez-Ullate Oteiza, David; Milson, RobertExceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of "exceptional" degrees. In this paper we introduce a new construction of multi-parameter exceptional Legendre polynomials by considering the isospectral deformation of the classical Legendre operator. Using confluent Darboux transformations and a technique from inverse scattering theory, we obtain a fully explicit description of the operators and polynomials in question. The main novelty of the paper is the novel construction that allows for exceptional polynomial families with an arbitrary number of real parameters. PublicationValidating ocean general circulation models via Lagrangian particle simulation and data from drifting buoys(Springer, 2019) Bedi, Karan; Gómez-Ullate Oteiza, David; Izquierdo, Alfredo; Fernández Montblanc, TomásDrifting Fish Aggregating Devices (dFADs) are small drifting platforms with an attached solar powered buoy that report their position with daily frequency via GPS. We use data of 9,440 drifting objects provided by a buoys manufacturing company, to test the predictions of surface current velocity provided by two of the main models: the NEMO model used by Copernicus Marine Environment Monitoring Service (CMEMS) and the HYCOM model used by the Global Ocean Forecast System (GOFS). PublicationCorrigendum on the proof of completeness for exceptional Hermite polynomials.(Academic Press Inc Elsevier Science, 2020-05) Gómez-Ullate Oteiza, David; Grandati, Yves; Milson, RobertExceptional orthogonal polynomials are complete families of orthogonal polynomials that arise as eigenfunctions of a Sturm-Liouville problem. Antonio Duran discovered a gap in the original proof of completeness for exceptional Hermite polynomials, that has propagated to analogous results for other exceptional families In this paper we provide an alternative proof that follows essentially the same arguments, but provides a direct proof of the key lemma on which the completeness proof is based. This direct proof makes use of the theory of trivial monodromy potentials developed by Duistermaat and Grtinbaum and Oblomkov. (C) 2019 Published by Elsevier Inc. PublicationA Bochner type characterization theorem for exceptional orthogonal polynomials(Elsevier science, 2019-04-01) García Ferrero, María Ángeles; Gómez-Ullate Oteiza, David; Milson, RobertIt was recently conjectured that every system of exceptional orthogonal polynomials is related to a classical orthogonal polynomial system by a sequence of Darboux transformations. In this paper we prove this conjecture, which paves the road to a complete classification of all exceptional orthogonal polynomials. In some sense, this paper can be regarded as the extension of Bochner's result for classical orthogonal polynomials to the exceptional class. As a supplementary result, we derive a canonical form for exceptional operators based on a bilinear formalism, and prove that every exceptional operator has trivial monodromy at all primary poles.