On convergence of subspaces generated by dilations of polynomials. An application to best local approximation

• Autores: Fabian E. Levis, Claudia V. Ridolfi
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 1, 2020, págs. 49-62
• Idioma: inglés
• DOI: 10.33044/revuma.v61n1a02
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We study the convergence of a net of subspaces generated by dilations of polynomials in a finite dimensional subspace. As a consequence, we extend the results given by Z´o and Cuenya [Advanced Courses of Mathematical Analysis II (Granada, 2004), 193–213, World Scientific, 2007] on a general approach to the problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials.

• Referencias bibliográficas
  • Billingsley, P., Convergence of Probability Measures, John Wiley & Sons, New York, 1968. MR 0233396.
  • Chui, C.K., Shisha, O., Smith, P.W., Best local approximation, J. Approx. Theory 15 (1975), no. 4, 371–381. MR 0433101.
  • Chui, C.K., Smith, P.W., Ward, J.D., Best L2 approximation, J. Approx. Theory 22 (1978), no. 3, 254–261. MR 0510758.
  • Chui, C.K., Diamond, H., Raphael, L.A., Best local approximation in several variables, J. Approx. Theory 40 (1984), no. 4, 343–350. MR 0740646.
  • Cuenya, H.H., Ferreyra, D.E., Cp condition and the best local approximation, Anal. Theory Appl. 31 (2015), no. 1, 58–67. MR 3338788.
  • Favier, S., Convergence of function averages in Orlicz spaces, Numer. Funct. Anal. Optim. 15 (1994), no. 3-4, 263–278. MR 1272205.
  • Feller, W., An Introduction to Probability and Its Applications, Vol. II, John Wiley & Sons, New York, 1966. MR 021015
  • Headley, V.B., Kerman, R.A., Best local approximations in Lp(µ), J. Approx. Theory 62 (1990), no. 3, 277–281. MR 1070281.
  • Mac´ıas, R.A., Z´o, F., Weighted best local Lp approximation, J. Approx. Theory 42 (1984), no. 2, 181–192. MR 0760741.
  • Maehly, H., Witzgall, Ch., Tschebyscheff-Approximationen in kleinen Intervallen. I. Approximation durch Polynome, Numer. Math. 2 (1960), 142–150....
  • Walsh, J.L., On approximation to an analytic function by rational functions of best approximation. Math. Z. 38 (1934), no. 1, 163–176. MR...
  • Wolfe, J.M., Interpolation and best Lp local approximation. J. Approx. Theory 32 (1981), no. 2, 96–102. MR 0633695.
  • Zó, F., Cuenya, H.H., Best approximations on small regions. A general approach. In: Advanced Courses of Mathematical Analysis II (Granada,...