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

Three term relations formultivariate Uvarov orthogonal polynomials

Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by a Uvarov modification of a givenmoment functional are studied. Existence of Uvarov orthogonal polynomials is analyzed, stating conditions to ensure it. The matrices of the three term relations of the Uvarov orthogonal polynomials are explicitly given in terms of the matrices of the three term relations satisfied by the original family. Two examples are presented in order to show that the results are valid for positive definite linear functionals and also for some quasi definite linear functionals which are not positive definite.Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) 120F140Spanish Government PID2020-113275GB-I00European CommissionFEDER/J. Andalucia A-FQM-246-UGR20MCIN/AEI PGC2018-094932-B-I00European Commission PGC2018-094932-B-I00IMAG-Maria de Maeztu grant CEX2020-001105-

Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations

We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyse relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differentialdifference equation for the bivariate orthogonal polynomials is deduced. The extension of the Painlev´e equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained.Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) 88887.310463/2018-00 88887.575407/2020-00FEDER/Junta de Andalucia A-FQM-246-UGR20MCIN PGC2018-094932B-I00European CommissionIMAG-Maria de Maeztu grant CEX2020-00 1105-

Capital cultural y capitales europeas de la cultura: la experiencia de La Villa de La Orotava

A continuación se dispone a presentar las siguientes cuestiones: ¿Cómo afecta la cultura a las ciudades? ¿Es suficiente la inversión que se realiza actualmente en este ámbito? Se analizará cómo el conocimiento y la divulgación del patrimonio histórico y la cultura, en las diversas formas en las que se nos presenta, sirve de vía de impulso para el desarrollo local y económico de una sociedad. En primer lugar, se presentará la distinción de ciudad Capital Europea de la Cultura y se señalarán algunos ejemplos de ciudades galardonadas, en las que se explicará y se mostrará los diferentes cambios que surgieron a raíz de su nombramiento. Por otro lado, se procederá a detallar y definir los diferentes aspectos de la cultura del municipio de La Villa de La Orotava. Realizando especial hincapié en uno de los mayores espacios de cultura e historia, se trata de los museos.The proyect below is about to summit the next questions: How does culture affect cities? Are nowadays investments enough on this scope? How knowledge and divulgation on historical heritage and culture, in the various forms they are known by society, work as an engine for local and economic development of partnerships, are now going to be analized. Firstly, it will be explained the concept of Europan Capital of Culture and they will be pointed out some examples of cities designated like that, on which it will be shown and exposed the many changes that happened as a consequence of its commition. On the other hand, they will be detailed and defined some aspects of La Villa de La Orotava’s culture. In order to do this, it will be mention one of the most important places of culture and history, which are museum

Obstrucción al flujo de la unión esofagogástrica: carecterización de una entidad recientemente descrita mediante manometría esofágica de alta resolución

Tesis doctoral inedita leída en la Universidad Autónoma de Madrid, Facultad de Medicina, Departamento de Medicina. Fecha de lectura: 12/06/201

Sobolev orthogonal polynomials and spectral methods in boundary value problems

The work by FM has been supported by FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación of Spain, grant PID2021-122154NB-I00, and the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors, grant EPUC3M23 in the context of the V PRICIT (Regional Program of Research and Technological Innovation). LF, TEP and MAP thanks Grant FQM-246-UGR20 funded by Consejería de Universidad, Investigación e Innovación and by European Union NextGenerationEU/PRTR; and Grant CEX2020-001105-M funded by MCIN/AEI/10.13039/501100011033. Funding for APC: Universidad Carlos III de Madrid (Agreement CRUE-Madroño 2023).In the variational formulation of a boundary value problem for the harmonic oscillator, Sobolev inner products appear in a natural way. First, we study the sequences of Sobolev orthogonal polynomials with respect to such an inner product. Second, their representations in terms of a sequence of Gegenbauer polynomials are deduced as well as an algorithm to generate them in a recursive way is stated. The outer relative asymptotics between the Sobolev orthogonal polynomials and classical Legendre polynomials is obtained. Next we analyze the solution of the boundary value problem in terms of a Fourier-Sobolev projector. Finally, we provide numerical tests concerning the reliability and accuracy of the Sobolev spectral method.FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación of Spain PID2021-122154NB-I00Madrid Government EPUC3M23Consejería de Universidad, Investigación e Innovación FQM-246-UGR20European Union NextGenerationEU/PRTRMCIN/AEI/10.13039/501100011033: CEX2020-001105-MUniversidad Carlos III de Madrid CRUE-Madroño 202

Simultaneous Approximation via Laplacians on the Unit Ball

We study the orthogonal structure on the unit ball Bd of Rd with respect to the Sobolev inner products f, g Δ = λL(f, g) + Bd Δ[(1 − x 2)f(x)] Δ[(1 − x 2)g(x)] dx, where L(f, g) = Sd−1 f(ξ) g(ξ) dσ(ξ) or L(f, g) = f(0)g(0), λ > 0, σ denotes the surface measure on the unit sphere Sd−1, and Δ is the usual Laplacian operator. Our main contribution consists in the study of orthogonal polynomials associated with ·, · Δ, giving their explicit expression in terms of the classical orthogonal polynomials on the unit ball, and proving that they satisfy a fourth-order partial differential equation, extending the well-known property for ball polynomials, since they satisfy a second-order PDE.We also study the approximation properties of the Fourier sums with respect to these orthogonal polynomials and, in particular, we estimate the error of simultaneous approximation of a function, its partial derivatives, and its Laplacian in the L2(Bd) space.Funding for open access publishing: Universidad de Granada/CBUAFunding for open access charge: Universidad de Granad

RODRÍGUEZ LÓPEZ, B.; SÁNCHEZ MADRID, N..; ZAHARIJEVIĆ, A. (eds.). (2021). Rethinking Vulnerability and Exclusion: Historical and Critical Essays. Suiza: Palgrave Macmillan.

Reseña de: RODRÍGUEZ LÓPEZ, B.; SÁNCHEZ MADRID, N..; ZAHARIJEVIĆ, A. (eds.). (2021). Rethinking Vulnerability and Exclusion: Historical and Critical Essays. Suiza: Palgrave Macmillan