GENERATORS OF MEHLER-TYPE SEMIGROUPS AS PSEUDO-DIFFERENTIAL OPERATORS
2002 ◽
Vol 05
(03)
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pp. 297-315
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Keyword(s):
We study semigroups (Pt)t ≥ 0 on a Hilbert space E, given by a Mehler-type formula: [Formula: see text] Under reasonable assumptions, the Lp(E,μ)-generator [Formula: see text] of (Pt)t ≥ 0 turns out to be expressible as a pseudo-differential operator, provided μ is an invariant measure for (Pt)t ≥ 0. The question of Lp-uniqueness is also answered positively.
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