Democracy functions and optimal embeddings for approximation spaces
نویسندگان
چکیده
We prove optimal embeddings for nonlinear approximation spaces Aq , in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for N -term wavelet approximation in L, Orlicz, and Lorentz norms. We also study the “greedy classes” G α q introduced by Gribonval and Nielsen, obtaining new counterexamples which show that G α q 6= Aq for most non democratic unconditional bases.
منابع مشابه
Spaces of generalized smoothness in the critical case: Optimal embeddings, continuity envelopes and approximation numbers
We study necessary and sufficient conditions for embeddings of Besov spaces of generalized smoothness B p,q (Rn) into generalized Hölder spaces Λ μ(·) ∞,r(R) when s(Nτ−1) > 0 and τ−1 ∈ `q′ , where τ = σN−n/p. A borderline situation, corresponding to the limiting situation in the classical case, is included and give new results. In particular, we characterize optimal embeddings for B-spaces. As ...
متن کاملDemocracy functions of wavelet bases in general Lorentz spaces
We compute the democracy functions associated with wavelet bases in general Lorentz spaces Λw and Λ q,∞ w , for general weights w and 0 < q <∞.
متن کاملOptimal coincidence best approximation solution in non-Archimedean Fuzzy Metric Spaces
In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuz...
متن کاملA Numerical Approach for Fractional Optimal Control Problems by Using Ritz Approximation
In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the num...
متن کاملRandomized approximation of Sobolev embeddings, III
We continue the study of randomized approximation of embeddings between Sobolev spaces on the basis of function values. The source space is a Sobolev space with nonnegative smoothness order, the target space has negative smoothness order. The optimal order of approximation (in some cases only up to logarithmic factors) is determined. Extensions to Besov and Bessel potential spaces are given and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Adv. Comput. Math.
دوره 37 شماره
صفحات -
تاریخ انتشار 2012