http://hdl.handle.net/10016/5859 2013-05-26T02:48:06Z http://hdl.handle.net/10016/6935 Title: Recent trends in orthogonal polynomials and their applications Author(s): Marcellán, Francisco; Arvesú, Jorge Abstract: In this contribution we summarize some new directions in the theory of orthogonal polynomials. In particular, we emphasize three kinds of orthogonality conditions which have attracted the interest of researchers from the last decade to the present time. The connection with operator theory, potential theory and numerical analysis will be shown. Description: 29 pages, 1 figure.-- MSC2000 codes: 42C05, 33C45.-- Contributed to: XVII CEDYA: Congress on differential equations and applications/VII CMA: Congress on applied mathematics (Salamanca, Spain, Sep 24-28, 2001).; MR#: MR1873645 (2002i:42031); Zbl#: Zbl 1026.42025 2000-12-31T23:00:00Z http://hdl.handle.net/10016/6657 Title: On the stability of recurrence relations for hypergeometric functions Author(s): Deaño, Alfredo; Segura, Javier Abstract: We consider the three term recurrence relations y_n+1 + a_n y_n + b_n y_n-1 = 0 satisfied simultaneously by confluent hypergeometric functions M(a+kn; c+mn; x) and U(a+kn; c+mn; x) (up to normalizations not depending on x). The parameters a, c, x are fixed and k,m = 0,±1. The existence of minimal solutions when n -> ∞ is a crucial piece of information when we intend to use a recurrence relation for computation. However, in some cases the behavior of the solutions for moderate values of n can be opposite to the asymptotic behaviour. We provide numerical examples of this phenomenon, already noted by W. Gautschi in the case (k,m) = (1,1), both for the recurrence relations and for the associated continued fractions. Description: 4 pages, no figures.-- MSC2000 codes: 33C15, 33F05, 40A15.-- Running title: "Recurrences and continued fractions for Kummer functions".; Contributed to: ICNAAM 2005: Official conference of the European Society of Computational Methods in Sciences and Engineering (Rhodes, Greece, Sep 16-20, 2005).; Zbl#: Zbl 1086.33007 2004-12-31T23:00:00Z http://hdl.handle.net/10016/6571 Title: Asymptotic behavior of orthogonal polynomials primitives Author(s): Fundora, Alfredo; Pijeira, Héctor; Urbina, Wilfredo Abstract: We study the zero location and the asymptotic behavior of the primitives of the standard orthogonal polynomials with respect to a finite positive Borel measure concentrate on [−1,1]. Description: 7 pages, no figures.-- MSC2000 codes: 42C05, 33C25. 2000-12-31T23:00:00Z http://hdl.handle.net/10016/6490 Title: Approximation theory for weighted Sobolev spaces on curves Author(s): Álvarez, Venancio; Pestana, Domingo; Rodríguez, José M.; Romera, Elena Abstract: In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials. Description: 17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.; MR#: MR1882649 (2003c:42002) 2000-12-31T23:00:00Z