, Volume 83, Issue 1, pp 88-96

Approximate Carleman theorems and a Denjoy-Carleman maximum principle

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Abstract.

We give an extension of the Denjoy-Carleman theorem, which leads to a generalization of Carleman’s theorem on the unique determination of probability measures by their moments. We also give complex versions of Carleman’s theorem extending Theorem 4.1 of [2].

Received: 12 September 2003; revised manuscript accepted: 17 December 2003