Of concern are multiplicative perturbations of the Laplacian acting on weighted spaces of continuous functions on R^N. It is proved that such differential operators, defined on their maximal domains, are pre-generators of positive quasicontractive C_0-semigroups of operators that fulfil the Feller property. Accordingly, these semigroups are associated with a suitable probability transition function and hence with a Markov process on R^N. An approximation formula for these semigroups is also stated in terms of iterates of integral operators that generalize the classical Gauss-Weierstrass operators. Some applications of such approximation formula are finally shown concerning both the semigroups and the associated Markov processes.
Multiplicative perturbations of the Laplacian and related approximation problems, to appear in Journal of Evolution Equations
ALTOMARE, Francesco;
2011-01-01
Abstract
Of concern are multiplicative perturbations of the Laplacian acting on weighted spaces of continuous functions on R^N. It is proved that such differential operators, defined on their maximal domains, are pre-generators of positive quasicontractive C_0-semigroups of operators that fulfil the Feller property. Accordingly, these semigroups are associated with a suitable probability transition function and hence with a Markov process on R^N. An approximation formula for these semigroups is also stated in terms of iterates of integral operators that generalize the classical Gauss-Weierstrass operators. Some applications of such approximation formula are finally shown concerning both the semigroups and the associated Markov processes.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
