# Asymptotics of sums of subcoercive operators

Nick Dungey; A. ter Elst; Derek Robinson

Colloquium Mathematicae (1999)

- Volume: 82, Issue: 2, page 231-260
- ISSN: 0010-1354

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topDungey, Nick, ter Elst, A., and Robinson, Derek. "Asymptotics of sums of subcoercive operators." Colloquium Mathematicae 82.2 (1999): 231-260. <http://eudml.org/doc/210760>.

@article{Dungey1999,

abstract = {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.},

author = {Dungey, Nick, ter Elst, A., Robinson, Derek},

journal = {Colloquium Mathematicae},

keywords = {subcoercive operators; connected Lie group; Riesz transforms; nilpotent Lie groups},

language = {eng},

number = {2},

pages = {231-260},

title = {Asymptotics of sums of subcoercive operators},

url = {http://eudml.org/doc/210760},

volume = {82},

year = {1999},

}

TY - JOUR

AU - Dungey, Nick

AU - ter Elst, A.

AU - Robinson, Derek

TI - Asymptotics of sums of subcoercive operators

JO - Colloquium Mathematicae

PY - 1999

VL - 82

IS - 2

SP - 231

EP - 260

AB - 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.

LA - eng

KW - subcoercive operators; connected Lie group; Riesz transforms; nilpotent Lie groups

UR - http://eudml.org/doc/210760

ER -

## References

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