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.File in questo prodotto:
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