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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics // Archive

Izv. Saratov Univ. Math. Mech. Inform., 2014 Volume 14, Issue 4(2), Pages 497–505 (Mi isu541)

Mathematics

On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables

N. Yu. Antonov

N. N. Krasovskii Institute of Mathematics and Mechanics UB RAS, 16, S. Kovalevskoy str., Ekaterinburg, 620990, Russia

Abstract: We consider one type of convergence of double trigonometric Fourier series intermediate between convergence over squares and $\lambda$-convergence for $\lambda>1$. We construct an example of continuous functions of two variables, Fourier series of which diverges in this sense, almost everywhere.

Key words: multiple Fourier series, almost everywhere convergence.

UDC: 517.518

DOI: 10.18500/1816-9791-2014-14-4-497-505



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