Logo image
The heat semigroup and integrability of Lie algebras
Journal article   Open access   Peer reviewed

The heat semigroup and integrability of Lie algebras

Ola Bratteli, Frederick M Goodman, Palle E.T Jørgensen and Derek W Robinson
Journal of functional analysis, Vol.79(2), pp.351-397
1988
DOI: 10.1016/0022-1236(88)90018-3
url
https://doi.org/10.1016/0022-1236(88)90018-3View
Published (Version of record) Open Access

Abstract

Let (∥dU(x 1 S t ∥⩽c/t 1 2 , 0 < ⩽ 1) denote a continuous representation U of a Lie group G acting on a Banach space B and S the semigroup generated by the closed Laplacian associated with a basis of the Lie algebra g in the derived representation dU . We prove there is a c > 0 such that ∥dU(x i ) S t ∥ ⩽ c t 1 2 , 0 < t ⩽ 1 , for all x i in the basis of g , and we also prove that this property is characteristic for integrability of a Lie algebra of operators satisfying the usual dissipativity requirements for generators of one-parameter groups. The basic estimate is established from bounds on the heat kernel associated with S.

Details

Metrics

Logo image