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Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator
In this paper we study the Fokker-Planck operator with potential V(x), and
analyze some kind of conditions imposed on the potential to ensure the validity
of global hypoelliptic estimates. As a consequence, we obtain the compactness
of resolvent of the Fokker-Planck operator if either the Witten Laplacian on
0-forms has a compact resolvent or some additional assumption on the behavior
of the potential at infinity is fulfilled. This work improves the previous
results of H\'erau-Nier and Helffer-Nier, by obtaining a better global
hypoelliptic estimate under weaker assumptions on the potential.Comment: Lemma 4.6 is correcte
Is the partner of in the nonet?
Based on a mass matrix, the mixing angle of the axial vector
states and is determined to be , and the
theoretical results about the decay and production of the two states are
presented. The theoretical results are in good agreement with the present
experimental results, which suggests that can be assigned as the
partner of in the nonet. We also suggest that
the existence of needs further experimental confirmation.Comment: Latex, 6 pages, to be published in Chin. Phys. let
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