Geodesic
Mean value densities for temperatures
N. Suzuki1 ; N. A. Watson2
1 Graduate School of Mathematics Nagoya University Nagoya, Japan
2 Department of Mathematics and Statistics University of Canterbury Christchurch, New Zealand
Colloquium Mathematicum, Tome 98 (2003) no. 1, pp. 87-96 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A positive measurable function $K$ on a domain $D$ in ${{\mathbb R}}^{n+1}$ is called a mean value density for temperatures if $u(0,0) = \int \int _D K(x,t)u(x,t)\, dx\, dt$ for all temperatures $u$ on $\, \overline {\! D}$. 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.
DOI : 10.4064/cm98-1-7
Keywords: positive measurable function domain mathbb called mean value density temperatures int int t temperatures overline construct density domains existence bounded density density which bounded away zero discussed

N. Suzuki 1 ; N. A. Watson 2

1 Graduate School of Mathematics Nagoya University Nagoya, Japan
2 Department of Mathematics and Statistics University of Canterbury Christchurch, New Zealand 
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N. Suzuki; N. A. Watson. Mean value densities for temperatures. Colloquium Mathematicum, Tome 98 (2003) no. 1, pp. 87-96. doi: 10.4064/cm98-1-7

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