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A Convergence Theorem for Double L2 Fourier Series
Published online by Cambridge University Press: 20 November 2018
Extract
Our aim in this paper is to extend a known theorem about the convergence of subsequences of the partial sums of the Fourier series in one variable of class L2 to Fourier series in two variables of the same class, (1, p. 396). The theorem asserts that for each function ƒ in L2, there is a sequence {mV} of positive integers of upper density one such that
Smv(X;ƒ)
converges to ƒ almost everywhere where sm(x;f) denotes the mth partial sum of the Fourier series of ƒ.
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- Copyright © Canadian Mathematical Society 1958
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