منابع مشابه
Democratic systems of translates
Democratic systems arise in the context of greedy approximations in Banach spaces. The greedy algorithm is an important method in numerical mathematics; for more details see the early work of V. N. Temlyakov [16], [17]. At the same time it also points to some interesting issues in functional analysis. In particular, we would like to emphasize the basic theorem of S. V. Konyagin and V. N. Temlya...
متن کاملSYSTEMS FORMED BY TRANSLATES OF ONE ELEMENT IN Lp(R)
Abstract. Let 1 ≤ p < ∞, f ∈ Lp(R) and Λ ⊆ R. We consider the closed subspace of Lp(R), Xp(f,Λ), generated by the set of translations f(λ) of f by λ ∈ Λ. If p = 1 and {f(λ) : λ ∈ Λ} is a bounded minimal system in L1(R), we prove that X1(f,Λ) embeds almost isometrically into `1. If {f(λ) : λ ∈ Λ} is an unconditional basic sequence in Lp(R), then {f(λ) : λ ∈ Λ} is equivalent to the unit vector ba...
متن کاملOrthogonal Frames of Translates
Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in L(R). The characterizations are applied to Bessel sequences which have an affine struc...
متن کاملFrames of Translates
Frames consisting of translates of a single function play an important role in sampling theory as well as in wavelet theory and Gabor analysis. We give a necessary and sufficient condition for a subfamily of regularly spaced translates of a function φ ∈ L(R), (τnbφ)n∈Λ, Λ ⊂ Z, to form a frame (resp. Riesz basis) for its closed linear span. One consequence is that if Λ ⊂ N , then this family is ...
متن کاملTranslates of Linear Codes Over
We give a method to compute the complete weight distribution of translates of linear codes over Z4. The method follows known ideas that have already been used successfully by others for Hamming weight distributions. For the particular case of quaternary Preparata codes, we obtain that the number of distinct complete weights for the dual Preparata codes and the number of distinct complete coset ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2013
ISSN: 0021-9045
DOI: 10.1016/j.jat.2013.03.001