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On the generalizations of the theorems of Parseval and Riesz-Fischer

Published online by Cambridge University Press:  24 October 2008

S. Pollard
S. Pollard
Affiliation:
Trinity College
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Extract

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Any two real numbers p and q will be called conjugate if

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 8 , October 1927 , pp. 865 - 870
Copyright
Copyright © Cambridge Philosophical Society 1927

References

* Hobson, E. W., Theory of Functions of a Real Variable, 2 (1926), 599–606.Google Scholar

* By (4·1) is to be understood that f(x) = g(x) throughout −π ≤ x ≤ π except possibly at the points of a set of measure zero.

* Banach, S., Proc. London Math. Soc. (2) 21 (1923), 95–97. Banach assumes that f(x) is positive and so absolutely integrable. It is interesting to verify that his construction can be extended to the case of conditionally integrable functions.CrossRefGoogle Scholar