Abstract
We develop the multidimensional functional calculus of semigroup generators which is based on the class of Bernstein functions in several variables. We establish spectral mapping theorems, give a holomorphy condition for the semigroups generated by the operators arising in this calculus, as well as prove the moment inequality for these operators.
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Original Russian Text Copyright © 2011 Mirotin A. R.
The author was supported in part by the Belarussian Republic Foundation of Fundamental Researches (Grant 20061473).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 6, pp. 1300–1312, November–December, 2011.
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Mirotin, A.R. On some properties of the multidimensional Bochner-Phillips functional calculus. Sib Math J 52, 1032–1041 (2011). https://doi.org/10.1134/S0037446611060085
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DOI: https://doi.org/10.1134/S0037446611060085