2009•Mathematical NotesRequires access
On the uniqueness and integrability of multiple trigonometric series
Aleksandr Andranikovich Talalyan
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Abstract
Under minimal constraints on the coefficients, we prove uniqueness theorems for multiple trigonometric series in which, instead of pointwise convergence, we consider the convergence of integral means of spherical, cubic, and other partial sums. We also obtain sufficient conditions for the integrability of multiple trigonometric series, i.e., conditions under which these series are Fourier series.