Fourier series of Gegenbauer-Sobolev polynomials

Autor: Ciaurri Ramírez, OscarMínguez Ceniceros, Judit

Tipo de documento: Artículo de revista

Revista: Symmetry, Integrability and Geometry: Methods and Applications. ISSN: 1815-0659. Año: 2018. Volumen: 14.

doi 10.3842/SIGMA.2018.024

CIRC: GRUPO A

Referencias:

  • Bavinck, H., Meijer, H.G., Orthogonal polynomials with respect to a symmetric inner product involving derivatives (1989) Appl. Anal, 33, pp. 103-117
  • Fejzullahu, B.X., Marcellán, F., A Cohen type inequality for Gegenbauer-Sobolev expansions (2013) Rocky Mountain J. Math, 43, pp. 135-148
  • Guadalupe, J.J., Pérez, M., Ruiz, F.J., Varona, J.L., Weighted Lp-boundedness of Fourier series with respect to generalized Jacobi weights (1991) Publ. Mat, 35, pp. 449-459
  • Guadalupe, J.J., Pérez, M., Ruiz, F.J., Varona, J.L., Weighted norm inequalities for polynomial expansions associated to some measures with mass points (1996) Constr. Approx, 12, pp. 341-360. , math.CA/9505214
  • Marcellán, F., Quintana, Y., Urieles, A., On the Pollard decomposition method applied to some Jacobi-Sobolev expansions, Turkish (2013) J. Math, 37, pp. 934-948
  • Marcellán, F., Xu, Y., On Sobolev orthogonal polynomials (2015) Expo. Math, 33, pp. 308-352
  • Moreno, A.F., Marcellán, F., Osilenker, B.P., Estimates for polynomials orthogonal with respect to some Gegenbauer-Sobolev type inner product (1999) J. Inequal. Appl, 3, pp. 401-419
  • Muckenhoupt, B., Mean convergence of Jacobi series (1969) Proc. Amer. Math. Soc, 23, pp. 306-310
  • Muckenhoupt, B., Transplantation theorems and multiplier theorems for Jacobi series (1986) Mem. Amer. Math. Soc, 64, pp. 4-86
  • Nevai, P., Mean convergence of Lagrange interpolation. III (1984) Trans. Amer. Math. Soc, 282, pp. 669-698
  • Pollard, H., The mean convergence of orthogonal series. II (1948) Trans. Amer. Math. Soc, 63, pp. 355-367
  • Pollard, H., The mean convergence of orthogonal series. III (1949) Duke Math. J, 16, pp. 189-191
  • Rodríguez, J.M., Romera, E., Pestana, D., Alvarez, V., Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials. II (2002) Approx. Theory Appl, 18, pp. 1-32
  • Szegő, G., Orthogonal polynomials (1975) American Mathematical Society, 23. , Colloquium Publications, 4th ed., Amer. Math. Soc., Providence, R.I
  • Xu, Y., Mean convergence of generalized Jacobi series and interpolating polynomials. I (1993) J. Approx. Theory, 72, pp. 237-251
  • Xu, Y., Mean convergence of generalized Jacobi series and interpolating polynomials. II (1994) J. Approx. Theory, 76, pp. 77-92