Pseudodifferential operators with non-regular operator-valued symbols

Type of Publication: Working Paper/Technical Report
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-202597
Author: Barraza Martinez, Bienvenido,; Denk, Robert; Hernandez Monzon, Jairo,
Year of publication: 2012
Series: Konstanzer Schriften in Mathematik ; 307
Summary:
In this paper, we consider pseudodifferential operators with operator-valued symbols and their mapping properties, without assumptions on the underlying Banach space. We show that, under suitable parabolicity assumptions, the realization of the operator in the standard Sobolev space generates an analytic semigroup. An application to non-autonomous pseudodifferential Cauchy problems gives the existence and uniqueness of a classical solution. Our approach is based on oscillatory integrals and kernel estimates for them.
MSC Classification: 35S05, 47D06, 35R20
Subject (DDC): 510 Mathematics
Keywords: Pseudodifferential operators, operator-valued symbols, generation of analytic semigroup
Link to License: In Copyright
Bibliography of Konstanz: Yes

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BARRAZA MARTINEZ, Bienvenido, Robert DENK, Jairo HERNANDEZ MONZON, 2012. Pseudodifferential operators with non-regular operator-valued symbols

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