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Mean value densities for temperatures

N. Suzuki, N. A. Watson (2003)

Colloquium Mathematicae

A positive measurable function K on a domain D in n + 1 is called a mean value density for temperatures if u ( 0 , 0 ) = D K ( x , t ) u ( x , t ) d x d t for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.

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