Abstract
The investigation of the asymptotic behavior of trigonometric series near the origin is a prominent topic in mathematical analysis. For trigonometric series in one variable, this problem was exhaustively studied by various authors in a series of publications dating back to the work of G.H. Hardy, 1928. Trigonometric series in several variables have got less attention. The aim of the work is to find the asymptotics of trigonometric series in several variables with the terms, having a form of “one minus the cosine” accurate to a decreasing power factor.
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