Spectral condition, hitting times and Nash inequality
Eva Löcherbach, Oleg Loukianov, Dasha Loukianova (2014)
Annales de l'I.H.P. Probabilités et statistiques
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Let be a -symmetric Hunt process on a LCCB space . For an open set , let be the exit time of from and be the generator of the process killed when it leaves . Let and . We give necessary and sufficient conditions for in terms of the behavior near the origin of the spectral measure of . When , , by means of this condition we derive the Nash inequality for the killed process. In the diffusion case this permits to show that the existence of moments of order for ...