Set of Uniqueness
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Set of Uniqueness

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High Quality Content by WIKIPEDIA articles! In mathematics, a set of uniqueness is a concept relevant to trigonometric expansions which are not necessarily Fourier series. Their study is a relatively pure branch of harmonic analysis. The empty set is a set of uniqueness. This is just a fancy way to say that if a trigonometric series converges to zero everywhere then it is trivial. This was proved by Riemann, using a delicate technique of double formal integration; and showing that the resulting sum has some generalized kind of second derivative using Toeplitz operators. Later on, Cantor genera...