Uniqueness of Representation by Trigonometric Series
J. Marshall Ash · American Mathematical Monthly · 1989
In 1870 Georg Cantor proved that a 2π periodic complex valued function of a real variable coincides with the values of at most one trigonometric series. We present his proof and then survey some of the many one dimensional generalizations and extensions of Cantor's theorem. We also survey the situation in higher dimensions, where a great deal less is known.