Absolute convergence of double trigonometric Fourier series and Walsh-Fourier Series

Veres Antal
Absolute convergence of double trigonometric Fourier series and Walsh-Fourier Series.
[Thesis] (Unpublished)

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Abstract in foreign language

In the first part of our theses we give sufficient conditions for the absolute convergence of the double Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to double Fourier series. In the second part we give sufficient conditions for the absolute convergence of the double Walsh-Fourier series of a function. These sufficient conditions are formulated in terms of (either global or local) dyadic moduli of continuity and s-bounded fluctuation.

Item Type:	Thesis (Doctoral thesis (PhD))
Creators:	Veres Antal
Hungarian title:	Kettős trigonometrikus Fourier-sorok és Walsh-Fourier-sorok abszolút konvergenciája
Supervisor(s):	Supervisor Position, academic title, institution MTMT author ID Móricz Ferenc professzor emeritus, DSc, SZTE TTIK Bolyai Intézet UNSPECIFIED
Subjects:	01. Natural sciences > 01.01. Mathematics
Divisions:	Doctoral School of Mathematics > Doctoral School of Mathematics (1993-2021)
Discipline:	Natural Sciences > Mathematics and Computer Sciences
Language:	English
Date:	2011. November 11.
Item ID:	690
MTMT identifier of the thesis:	1919939
doi:	https://doi.org/10.14232/phd.690
Date Deposited:	2011. Feb. 21. 16:00
Last Modified:	2022. Oct. 13. 15:29
Depository no.:	B 4957
URI:	https://doktori.bibl.u-szeged.hu/id/eprint/690
Defence/Citable status:	Defended.

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