In this paper, we give a decomposition of the space of tempered distributions by the Cesaro norm, and for any a > 1/2 we construct directly from the exotic trace an infinite dimensional separable Hilbert space H-c,H-2a-1 on which the exotic trace plays the role as the usual trace. This implies that the Exotic Laplacian coincides with the Volterra-Gross Laplacian in the Boson Fock space Gamma(H-c,H-2a-1) over the Hilbert space H-c,H-2a-1. Finally we construct the Brownian motion naturally associated to the Exotic Laplacian of order 2a - 1 and we find an explicit expression for the associated heat semigroup.
Accardi, L., Ji, U., Saito, K. (2009). Exotic laplacians and associated stochastic processes. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 12(1), 1-19 [10.1142/S0219025709003513].
Exotic laplacians and associated stochastic processes
ACCARDI, LUIGI;
2009-03-01
Abstract
In this paper, we give a decomposition of the space of tempered distributions by the Cesaro norm, and for any a > 1/2 we construct directly from the exotic trace an infinite dimensional separable Hilbert space H-c,H-2a-1 on which the exotic trace plays the role as the usual trace. This implies that the Exotic Laplacian coincides with the Volterra-Gross Laplacian in the Boson Fock space Gamma(H-c,H-2a-1) over the Hilbert space H-c,H-2a-1. Finally we construct the Brownian motion naturally associated to the Exotic Laplacian of order 2a - 1 and we find an explicit expression for the associated heat semigroup.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.