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From 1911 until 1920, Fischer was professor at Erlangen, then from 1920 he worked at Cologne.
In 1907 Ernst Fischer studied orthonormal sequences of functions and gave necessary and sufficient conditions for a sequence of constants to be the Fourier coefficients of a square integrable function. This led to the concept of a Hilbert space. F Riesz published a similar result in the same year.
The theorem, now called the Riesz-Fischer theorem, is one of the great achievements of the Lebesgue theory of integration.
Reference (One book/article)