共查询到4条相似文献,搜索用时 0 毫秒
1.
A second look at the authors' [BDR1], [BDR2] characterization of the approximation order of a Finitely generated Shift-Invariant
subspace S(Φ) of L
2
(R
d
) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that
the set of 1-periodizations of the generators is linearly independent, such a space is shown to provide approximation order
k if and only if contains a ψ (necessarily unique) satisfying . The technical condition is satisfied, e.g., when the generators are at infinity for some ρ>k+d . In the case of compactly supported generators, this recovers an earlier result of Jia [J1], [J2].
March 19. 1996. Date revised: September 6, 1996. 相似文献
2.
A second look at the authors' [BDR1], [BDR2] characterization of the approximation order of a Finitely generated Shift-Invariant
(FSI) subspace of L
2(R
d
) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that
the set of 1-periodizations of the generators is linearly independent, such a space is shown to provide approximation order
k if and only if contains a (necessarily unique) satisfying for |j|<k , . The technical condition is satisfied, e.g., when the generators are at infinity for some >k+d. In the case of compactly supported generators, this recovers an earlier result of Jia [J1], [J2].
March 19, 1996. Dates revised: September 6, 1996, March 4, 1997. 相似文献
3.
Given a function f on [0,1] and a wavelet-type expansion of f , we introduce a new algorithm providing an approximation
$\tilde f of f with a prescribed number D of nonzero coefficients in its expansion. This algorithm depends only on the number of coefficients to be kept and not on
any smoothness assumption on f . Nevertheless it provides the optimal rate D
-α
of approximation with respect to the L
q
-norm when f belongs to some Besov space B
α
p,∈fty
whenever α>(1/p-1/q)
+
. These results extend to more general expansions including splines and piecewise polynomials and to multivariate functions.
Moreover, this construction allows us to compute easily the metric entropy of Besov balls.
June 21, 1996. Dates revised: April 9, 1998; October 14, 1998. Date accepted: October 20, 1998. 相似文献
4.
In a recent investigation [8] concerning the asymptotic behavior of Gram—Schmidt orthonormalization procedure applied to
the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz
system in arose. In this paper, we provide a sufficient condition to determine whether the nonnegative translates form a Riesz system
on . This result is applied to identify a large class of functions for which very general translates enjoy the Riesz basis property
in .
August 5, 1998. Date revised: August 25, 1999. Date accepted: January 11, 2000. 相似文献