Geodesic
Asymptotics of sums of subcoercive operators
Colloquium Mathematicum, Tome 82 (1999) no. 2, pp. 231-260 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel and the kernel corresponding to the lowest order homogeneous component. We also prove boundedness of a range of Riesz transforms with the range again determined by the highest and lowest orders. Finally we analyze similar properties on general groups of polynomial growth and establish positive results for local direct products of compact and nilpotent groups.
DOI : 10.4064/cm-82-2-231-260

Nick Dungey 1 ; A. ter Elst 1 ; Derek Robinson 1

1 
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Nick Dungey; A. ter Elst; Derek Robinson. Asymptotics of sums of subcoercive operators. Colloquium Mathematicum, Tome 82 (1999) no. 2, pp. 231-260. doi: 10.4064/cm-82-2-231-260

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