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Asymptotic expansions of the representation formulae for (C 0) m-parameter operator semigroups 1 . 2 |
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| Authors: | Mi. Zhou George A. Anastassiou |
| Affiliation: | Department of Mathematical Sciences , The University of Memphis , Memphis, TN, 38152, U.S.A. |
| Abstract: | In this paper, we expand asymptotically the general representation formulae for (C o) m-parameter operator semigroups. When we consider special semigroups, our results yield the asymptotic expansions for multivariate Feller operators. In particular, the asymptotic expansions for univariate and multivariate Bernstein operators are reobtained. See the related examples at the end. |
| Keywords: | asymptotic expansions multi-parameter operator semigroups representation formulae Banach space probabilistic approach multivibrate approximation modulus of continuity Primary 41A60 Primary 47D05 Primary 41A63 Secondary 41A65 Secondary 41A35 |