Pseudodifferential operators with variable order of differentiation generating Feller semigroups. (English) Zbl 0793.35139
The authors consider pseudodifferential operators of variable order, with symbol of the type \(a(x,\xi)=\langle \xi \rangle^{s+h(x)}\), where \(s \geq 0\) is a real number and \(h(x)\) is in the Schwartz space \({\mathcal S} (\mathbb{R}^ n)\). They assume in addition \(0<\inf \{s+h(x)\} \leq \sup \{s+h(x)\} \leq 2\). The action of the operator \(a(x,D)\) is studied on suitable weighted Sobolev spaces. As conclusive result, \(-a(x,D)\) is proved to be the generator of a Feller semigroup.
Reviewer: L.Rodino (Torino)
MSC:
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 47G30 | Pseudodifferential operators |
| 46N20 | Applications of functional analysis to differential and integral equations |
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