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On uniqueness of the additive segment functions and trigonometric series. (English. Russian original) Zbl 0838.42004
Math. Notes 56, No. 4, 1015-1022 (1994); translation from Mat. Zametki 56, No. 4, 38-47 (1994).
A segment of the space \(\mathbb{R}^d\) is any set of the form \(\prod^d_{k=1} [x_k, y_k ]\), where \(x_k\leq y_k\) for each \(k\). The author proves a uniqueness theorem for additive segment functions whose symmetric derivatives equal zero a.e., provided a weak type inequality is satisfied for the majorant of the derivatives. Relying on this result, he derives uniqueness theorems for multidimensional trigonometric series.
Reviewer: F.Móricz (Szeged)

MSC:
42B05 Fourier series and coefficients in several variables
42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
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