منابع مشابه
NON-EQUIVALENT GREEDY AND ALMOST GREEDY BASES IN `p
For 1 < p < ∞ and p 6= 2 we construct a family of mutually non-equivalent greedy bases in `p having the cardinality of the continuum. In fact, no basis from this family is equivalent to a rearranged subsequence of any other basis thereof. We are able to extend this statement to the spaces Lp and H1. Moreover, the technique used in the proof adapts to the setting of almost greedy bases where sim...
متن کاملOn the Existence of Almost Greedy Bases in Banach Spaces
We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X h...
متن کاملComments on the Paper ’on the Existence of Almost Greedy Bases in Banach Spaces’ By
Greedy algorithms are widely used in image processing and other applications. Let X be a real Banach space with a semi-normalized basis (en). An algorithm for n-term approximation produces a sequence of maps Fn : X → X such that, for each x ∈ X, Fn(x) is a linear combination of at most n of the basis elements (ej). Konyagin and Temlyakov [12] introduced the Thresholding Greedy Algorithm (TGA) (...
متن کاملRenorming spaces with greedy bases
In approximation theory one is often faced with the following problem. We start with a signal, i.e., a vector x in some Banach space X. We then consider the (unique) expansion ∑∞ i=1 xiei of x with respect to some (Schauder) basis (ei) of X. For example, this may be a Fourier expansion of x, or it may be a wavelet expansion in Lp. We then wish to approximate x by considering m-term approximatio...
متن کاملGreedy Bases for Besov Spaces
We prove that the Banach spaces (⊕n=1`p )`q , which are isomorphic to the Besov spaces on [0, 1], have greedy bases, whenever 1 ≤ p ≤ ∞ and 1 < q < ∞. Furthermore, the Banach spaces (⊕n=1`p )`1 , with 1 < p ≤ ∞, and (⊕n=1`p )c0 , with 1 ≤ p < ∞ do not have a greedy bases. We prove as well that the space (⊕n=1`p )`q has a 1-greedy basis if and only if 1 ≤ p = q ≤ ∞.
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ژورنال
عنوان ژورنال: Proceedings of the Steklov Institute of Mathematics
سال: 2018
ISSN: 0081-5438,1531-8605
DOI: 10.1134/s0081543818080102