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Is there a connection between carleman inequality discovred by T. Carleman in 1922 if I am not mistaken in his research on quasianalytic functions and what is called Carleman estimates used in the PDE theory (see the works of Taylor and Tataru).

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no connection, other than that it's the same Carleman. – Carlo Beenakker Sep 26 '13 at 6:58
Dear @user36539: In case it answers your question, perhaps you would consider accepting Willie Wong's answer by clicking the green check-mark? Thanks. That would "close off" this question and keep it from getting bumped to the front page automatically. – Ricardo Andrade Oct 31 '13 at 12:49

(CW post just to get this off the unanswered list)

As Carlo Beenakker remarked, the only connection is that they are named after the same Carleman.

The Carleman estimates are weighted energy estimates for partial differential equations. They are so named because of their use by Carleman in his 1939 paper on the uniqueness (unique continuation) of solutions for a certain system of first order PDEs.

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@RicardoAndrade The community bot prevention only works when someone bothers to upvote this CW answer. – Willie Wong Oct 31 '13 at 16:26

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