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On the uniqueness and integrability of multiple trigonometric series. (English. Russian original) Zbl 1192.42007
Math. Notes 86, No. 5, 716-728 (2009); translation from Mat. Zametki 86, No. 5, 761-775 (2009).
Summary: 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.

MSC:
 42B05 Fourier series and coefficients in several variables 42B08 Summability in several variables
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References:
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