Abstract
If u is a smooth periodic function with Fourier coefficients (a n ) ∞− ∞, then we know that the sequence (a n ) ∞− ∞ uniquely determines the function u; in fact, the partial sums $${u_N}\left( x \right) = \sum\limits_{ - N}^N {{a_n}} \exp \left( {inx} \right)$$ ((1)) of the Fourier series converge to u in the sense of P.KeywordsFourier SeriesUnit DiscDirichlet ProblemClassical SolutionHeat EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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