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On the question of Abel’s summability method for eigenfunction expansions. (Russian. English summary) Zbl 0693.40011

Summary: Abel’s summability method of expansions by eigenfunctions of the Laplace operator for different domains is investigated. An estimation is given of the deviation of the sum of an absolutely convergent series, figuring in Abel’s method, from the function whose Fourier series is summed. A special uniqueness theorem for multiple trigonometric series is proved.

MSC:

40G10 Abel, Borel and power series methods
42C15 General harmonic expansions, frames
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