A note on “Enlarging the functional space of decay estimates on semigroups”

I have just uploaded a note on the issue of “enlarging the functional space of decay estimates on semigroups”:

http://hal.archives-ouvertes.fr/hal-00440119/

http://fr.arxiv.org/abs/0912.1747/

This is part of long-term project which started with my paper hal-00076709 (arxiv-0605688) on how to obtain relaxation estimates in larger spaces than the usual “symmetrization” space for PDEs arising in statistical physics. A paper with M.P. Gualdani and S. Mischler developing a full abstract method will soon be available.

Here is the abstract:

This note briefly presents a new method for enlarging the functional space of a “spectral-gap-like” estimate of exponential decay on a semigroup. A particular case of the method was first devised in hal-00076709 for the spatially homogeneous Boltzmann equation, and a variant was used in Ref. hal-00124876 in the same context for inelastic collisions. We present a generalized abstract version of it, a short proof of the algebraic core of the method, and a new application to the Fokker-Planck equation. More details and other applications shall be found in the work in preparation Ref. [3] (another application to quantum kinetic theory can be found in the work in preparation Ref. [4]).

math/0605688

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