We consider the problem of the identification of real continuos functions defined on [0,1], by means of the sums of the values f(a/n) with a=1,...,n (this is Fine's problem). This is not possible, in general (Besicovitch example), but we prove that it may be the case under auxiliary condition. We also study the behavior of a well known exceptional function.

A number theoretic estimate of Davenport from a functional analytic viewpoint

CODECA', Paolo;NAIR, Mohan K.
1999

Abstract

We consider the problem of the identification of real continuos functions defined on [0,1], by means of the sums of the values f(a/n) with a=1,...,n (this is Fine's problem). This is not possible, in general (Besicovitch example), but we prove that it may be the case under auxiliary condition. We also study the behavior of a well known exceptional function.
1999
Codeca', Paolo; Nair, Mohan K.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/521099
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