Let f{hook} be a function in Lp(T), 1 ≤ p < +∞, or le f{hook} be a continuous function on the torus T if p = + ∞, and let Kn be the nth Fejér kernel. We prove that, although the sequence {∥f{hook} - Kn*f{hook}∥p} is not monotone in general, it still has a monotonicity property. Namely, if m < n, then ∥f{hook} - Kn*f{hook}∥p ≤ (2 + m n)| 2 p - 1|∥f{hook} - Km *f{hook}∥p. © 1989.

Colzani, L. (1989). Is the approximation of a function by its Fejér means monotone?. JOURNAL OF APPROXIMATION THEORY, 56(2), 152-154 [10.1016/0021-9045(89)90106-8].

Is the approximation of a function by its Fejér means monotone?

COLZANI, LEONARDO
1989

Abstract

Let f{hook} be a function in Lp(T), 1 ≤ p < +∞, or le f{hook} be a continuous function on the torus T if p = + ∞, and let Kn be the nth Fejér kernel. We prove that, although the sequence {∥f{hook} - Kn*f{hook}∥p} is not monotone in general, it still has a monotonicity property. Namely, if m < n, then ∥f{hook} - Kn*f{hook}∥p ≤ (2 + m n)| 2 p - 1|∥f{hook} - Km *f{hook}∥p. © 1989.
Articolo in rivista - Articolo scientifico
Plancherell formula; Fejér kernel; convolution
English
1989
56
2
152
154
none
Colzani, L. (1989). Is the approximation of a function by its Fejér means monotone?. JOURNAL OF APPROXIMATION THEORY, 56(2), 152-154 [10.1016/0021-9045(89)90106-8].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/19139
Citazioni
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
Social impact