Riesz-Fischer theorem

Riesz-Fischer theorem

[′rēsh ′fish·ər ‚thir·əm]
(mathematics)
The vector space of all real- or complex-valued functions whose absolute value squared has a finite integral constitutes a complete inner product space.
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This theorem entails the use of the Riesz-Fischer theorem, the Planeherel-Polya inequality, and a uniqueness theorem which in turn depends on properties of the indicator diagram for entire functions.
4] < [infinity], then by the Riesz-Fischer theorem [5, p193], the series