Abstract
Let a2π-periodic function f(x, y) be continuous in some neighbourhood of the point (x, y) except possibly along finitely many lines l 1 , l 2 , ..., lk terminating at (x, y). The problem of convergence of the Fourier series of f(x, y) at the point (x, y) is examined in some detail. It is established that under certain restrictions on the variation of f(x, y), and also on the lines l 1 , l 2 , ..., lk, the fourier series converges to a value bounded above by the limit superior, and below by the limit inferior of f(x+u, y+v), u, v →0, this value depending on the manner in which the series is summed.
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