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001-es BibID:	BIBFORM116007
035-os BibID:	(WoS)001094934800001 (Scopus)85175793998
Első szerző:	Gát György (matematikus)
Cím:	Almost everywhere divergence of Cesaro means of subsequences of partial sums of trigonometric Fourier series / György Gát
Dátum:	2024
ISSN:	0025-5831
Megjegyzések:	In this paper, we investigate the relationship between pointwise convergence of the arithmetic means corresponding to the subsequence of partial Fourier sums (Skjf:j is an element of N) (for f is an element of L1(T)) and the structure of the chosen subsequence of the sequence of natural numbers (kj: j is an element of N). More precisely, the problem we deal with is to provide necessary and sufficient conditions for a subsequence N of N that has the following property: for any subsequence N'= (kj: j is an element of N) of N and any f is an element of L1(T) one has 1N n-ary sumation j=1NSkjf(x) [rightarrow] f(x) for a.e. x is an element of T. A direct corollary of this paper's main theorem is that there exists a subsequence (kj) of the sequence of natural numbers and an integrable function f such that the arithmetic means of Skjf do not converge to f almost everywhere. This is a negative answer to a question that originated in an article by Zalcwasser in 1936 Zalcwasser (Stud. Math. 6, 82-88 (1936)) for some increasing sequences (kj) of natural numbers.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk
Megjelenés:	Mathematische Annalen. - 389 : 4 (2024), p. 4199-4231. -
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