Artículos de revistas
Entropy and Widths of Multiplier Operators on Two-Point Homogeneous Spaces
Registro en:
Constructive Approximation. Springer, v. 35, n. 2, n. 137, n. 180, 2012.
0176-4276
WOS:000300521500001
10.1007/s00365-011-9146-7
Autor
Kushpel, A
Tozoni, SA
Institución
Resumen
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) In this article we continue the development of methods of estimating n-widths and entropy of multiplier operators begun in 1992 by A. Kushpel (Fourier Series and Their Applications, pp. 49-53, 1992; Ukr. Math. J. 45(1): 59-65, 1993). Our main aim is to give an unified treatment for a wide range of multiplier operators. on symmetric manifolds. Namely, we investigate entropy numbers and n-widths of decaying multiplier sequences of real numbers. Lambda = {lambda(k)}(k=1)(infinity), |lambda(1)| >= |lambda(2)| >= ... , Lambda : L-p(M-d) -> L-q (M-d) on two-point homogeneous spaces M-d : S-d, P-d (R), P-d (C), Pd (H), P-16(Cay). In the first part of this article, general U(p)per and lower bounds are established for entropy and n-widths of multiplier operators. In the second part, different applications of these results are presented. In particular, we show that these estimates are order sharp in various important situations. For example, sharp order estimates are found for function sets with finite and infinite smoothness. We show that in the case of finite smoothness (i.e., |lambda(k)| (infinity)(k=1)|lambda(1)| >= |lambda(2)| >= ... , Lambda, k -> infinity), we have e(n)(Lambda U-p(S-d), L-q (S-d)) << d(n)(U-p(S-d), L-q (S-d)), n -> infinity, but in the case of infinite smoothness (i.e., |lambda k| (sic) e(-gamma kr), gamma > 0, 0 < r = 1, k.8), we have e(n)(Lambda U-p(S-d), Lq (Sd)) >> dn(dU(p)(S-d), Lq (Sd)), n -> 8 for different p and q, where U-p(S-d) denotes the closed unit ball of Lp(S-d). 35 2 137 180 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) FAPESP [03/10393-8, 07/56162-8]