Modifications of functions, Fourier coefficients and nonlinear approximation
- Yerevan State University, Yerevan (Armenia)
This work continues the author's investigations of the convergence of greedy algorithms from the standpoint of classical results on correction of functions. In particular, the following result is obtained: for each {epsilon}, 0<{epsilon}<1, there exists a measurable set E subset of [0,1) of measure |E|>1-{epsilon} such that for each function f element of L{sup 1}[0,1) a function f-tilde element of L{sup 1}(0,1) equal to f on E can be found such that the greedy algorithm for f-tilde with respect to the Walsh system converges to it almost everywhere on [0,1], and all the nonzero elements of the sequence of Walsh-Fourier coefficients of the function thus obtained are arranged in decreasing order of their absolute values. Bibliography: 35 titles.
- OSTI ID:
- 21612776
- Journal Information:
- Sbornik. Mathematics, Vol. 203, Issue 3; Other Information: DOI: 10.1070/SM2012v203n03ABEH004226; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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