Pseudodifferential operators with non-regular operator-valued symbols

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307_Barraza_Denk.pdf
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2012
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Barraza Martinez, Bienvenido,
Hernandez Monzon, Jairo,
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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.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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Pseudodifferential operators, operator-valued symbols, generation of analytic semigroup
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ISO 690BARRAZA MARTINEZ, Bienvenido, Robert DENK, Jairo HERNANDEZ MONZON, 2012. Pseudodifferential operators with non-regular operator-valued symbols
BibTex
@techreport{BarrazaMartinez2012Pseud-20259,
  year={2012},
  series={Konstanzer Schriften in Mathematik},
  title={Pseudodifferential operators with non-regular  operator-valued symbols},
  number={307},
  author={Barraza Martinez, Bienvenido, and Denk, Robert and Hernandez Monzon, Jairo,}
}
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