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On Hausdorff's proof of the extended Riesz-Fischer theorem

Published online by Cambridge University Press:  24 October 2008

S. Pollard
S. Pollard
Affiliation:
Trinity College.
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Extract

1. The extended Riesz-Fischer theorem, in the special case of the trigonometrical orthogonal system, states that, if a and β are real numbers such that

then

implies, whenever α ≤ 2, the existence of a solution of the system of integral equations,

such that

and further

When a = 2, this reduces to the original Riesz-Fischer theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 5 , July 1925 , pp. 777 - 778
Copyright
Copyright © Cambridge Philosophical Society 1925

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References

* Hausdorff, , ‘Eine Ausdehnung des Parsevalschen Satzes über Fourierreihen,” Math. Zeitschrift, 16 (1923), 163–169.CrossRefGoogle Scholar