This article is cited in 1 paper

Convergence of Double Fourier Series after a Change of Variable

A. A. Sahakian

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: In this paper, we prove that for any compact set $\Omega\subset C(\mathbb T^2)$ there exists a homeomorphism $\tau$ of the closed interval $\mathbb T=[-\pi,\pi]$ such that for an arbitrary function $f\in\Omega$ the Fourier series of the function $F(x,y)=f(\tau(x),\tau(y))$ converges uniformly on $C(\mathbb T^2)$ simultaneously over rectangles, over spheres, and over triangles.

UDC: 517.518

Received: 08.04.2002
Revised: 17.10.2002

DOI: 10.4213/mzm263

 English version: Mathematical Notes, 2003, 74:2, 255–265

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