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Note on Continuous Functionals

Published online by Cambridge University Press:  24 October 2008

S. Verblunsky
S. Verblunsky
Affiliation:
Magdalene College
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Extract

1. Let ℱ be a family of functions X (t) defined in (0, 2π). The functionals to be considered are of a particular class, namely those which define a correspondence between each function X of ℱ and a number which we denote by F(X). It is convenient to refer to F(X) as the functional.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 27 , Issue 1 , January 1931 , pp. 49 - 56
Copyright
Copyright © Cambridge Philosophical Society 1931

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References

* Math. Zeit. 5, pp. 186–221 (1919).Google Scholar

* Steinhaus, loc. cit., Hilfsatz 3.

* Loc. cit., Umkehrung des Parallelsatzes 3.

* Loc. cit., Umkehrung des Satzes 3.

† Loc. cit., Satz 3.

* Loc. cit., Parallelsatz 3.

† The case p = 2 is due to Fréchet; loc. cit., Satz 2.