Artículos de revistas
Multivariate Sobolev-type Orthogonal Polynomials
Registro en:
Jaen Journal On Approximation. , v. 3, n. 2, p. 241 - 259, 2011.
18893066
2-s2.0-84874869654
Autor
Mello M.V.
Paschoa V.G.
Perez T.E.
Pinar M.A.
Institución
Resumen
Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions. © 2011 Universidad de Jaén. 3 2 241 259 Abramowitz, M., Stegun, I.A., Handbook of mathematical functions with formulas (1972) graphs and mathematical tables, , eds., Ninth printing, Dover publications, New York Alfaro, M., Marcellán, F., Rezola, M.L., Ronveaux, A., On orthogonal polynomials of Sobolev type: algebraic properties and zeros (1992) SIAM J. Math. Anal., 23 (3), pp. 737-757 Dunkl, C.F., Xu, Y., Orthogonal polynomials of several variables (2001) Encyclopedia of Mathematics and its Applications, 81. , Cambridge University Press, Cambridge Evans, W.D., Littlejohn, L.L., Marcellán, F., Markett, C., Ronveaux, A., On recurrence relations for Sobolev orthogonal polynomials (1995) SIAM J. Math. Anal., 26 (2), pp. 446-467 Fernández, L., Pérez, T.E., Piñar, M.A., Xu, Y., Krall-type orthogonal polynomials in several variables (2010) J. Comput. Appl. Math., 233 (6), pp. 1519-1524 Foulquié, A., Marcellán, F., Strong asymptotics on the support of the measure of orthogonality for polynomials orthogonal with respect to a discrete Sobolev inner product (1997) Methods Appl. Anal., 4 (1), pp. 53-66 López, G., Marcellán, F., Van Assche, W., Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product (1995) Constr. Approx., 11 (1), pp. 107-137 Marcellán, F., Van Assche, W., Relative asymptotics for orthogonal polynomials with a Sobolev inner product (1993) J. Approx. Theory, 72 (2), pp. 193-209 Szegö, G., Orthogonal polynomials. Fourth edition, American Mathematical Society (1975) Colloquium Publications, 23. , American Mathematical Society, Providence, R.I Xu, Y., Asymptotics for orthogonal polynomials and Christoffel functions on a ball (1996) Methods Appl. Anal., 3 (2), pp. 257-272 Xu, Y., Summability of Fourier orthogonal series for Jacobi weight on a ball in Rd (1999) Trans. Amer. Math. Soc., 351 (6), pp. 2439-2458