Uniformly convergent Fourier series with universal power parts on closed subsets of measure zero
Khrushchev S.
March 2023Academic Press Inc.
Journal of Approximation Theory
2023#287
Given a closed subset E of Lebesgue measure zero on the unit circle T there is a function f on T with uniformly convergent symmetric Fourier series Sn(f,ζ)=∑k=−nnfˆ(k)ζk⇉Tf(ζ),such that for every continuous function g on E, there is a subsequence of partial power sums Sn+(f,ζ)=∑k=0nfˆ(k)ζkof f, which converges to g uniformly on E. Here fˆ(k)=∫Tζ̄kf(ζ)dm(ζ),and m is the normalized Lebesgue measure on T.
Continuous functions , Convergence of Fourier series , Fourier series , Universal Fourier series
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Satbayev University, Department of Management and Mathematical Economics, 22a Satpaev str., Almaty, 050013, Kazakhstan
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