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Bernstein’s analyticity theorem for quantum differences

Tord Sjödin (2007)

Czechoslovak Mathematical Journal

We consider real valued functions $f$ defined on a subinterval $I$ of the positive real axis and prove that if all of $f$ ’s quantum differences are nonnegative then $f$ has a power series representation on $I$ . Further, if the quantum differences have fixed sign on $I$ then $f$ is analytic on $I$ .

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