Non-equivalent greedy and almost greedy bases inlp
نویسندگان
چکیده
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...
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We generalize several theorems of Rényi, Parry, Daróczy and Kátai by characterizing the greedy and quasi-greedy expansions in non-integer bases.
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Peixin Ye Nankai University, China [email protected] In this talk we discuss which properties of a basis are important for certain direct and inverse theorems in nonlinear approximation. We study greedy approximation with regard to bases with different properties. We consider bases that are tensor products of univariate greedy bases. Some results known for unconditional bases, such as Lebesgue...
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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...
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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...
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ژورنال
عنوان ژورنال: Journal of Function Spaces and Applications
سال: 2006
ISSN: 0972-6802
DOI: 10.1155/2006/368648