Multiplicative perturbations of the Laplacian and related approximation problems |
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Authors: | Francesco Altomare Sabina Milella Graziana Musceo |
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Affiliation: | (1) Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
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Abstract: | Of concern are multiplicative perturbations of the Laplacian acting on weighted spaces of continuous functions on mathbbRN, N 3 1{{mathbb{R}}^{N},; Ngeq1} . It is proved that such differential operators, defined on their maximal domains, are pre-generators of positive quasicontractive C 0-semigroups of operators that fulfill the Feller property. Accordingly, these semigroups are associated with a suitable probability transition function and hence with a Markov process on mathbbRN{{mathbb{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. |
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