In sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular, they are not a function of the control distance, nor they are for instance spherically symmetric in any of the layers of the Lie algebra. Despite these unfavourable aspects, in this paper we establish a new heat semigroup characterisation of the Sobolev and spaces in a Carnot group by means of an integral decoupling property of the heat kernel.
A Universal Heat Semigroup Characterisation of Sobolev and BV Spaces in Carnot Groups
Tralli, Giulio
2024
Abstract
In sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular, they are not a function of the control distance, nor they are for instance spherically symmetric in any of the layers of the Lie algebra. Despite these unfavourable aspects, in this paper we establish a new heat semigroup characterisation of the Sobolev and spaces in a Carnot group by means of an integral decoupling property of the heat kernel.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.