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Pseudodifferential operators with non-regular operator-valued symbols

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Abstract

In this paper, we consider pseudodifferential operators with operator-valued symbols and their mapping properties, without assumptions on the underlying Banach space E. We show that, under suitable parabolicity assumptions, the \({W_p^k(\mathbb{R}^n, E)}\)-realization of the operator generates an analytic semigroup. Our approach is based on oscillatory integrals and kernel estimates for them. An application to non-autonomous pseudodifferential Cauchy problems gives the existence and uniqueness of a classical solution. As an example, we include a discussion of coagulation–fragmentation processes.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del Norte, Km 5 Via a Puerto Colombia, Barranquilla, Colombia

    Bienvenido Barraza Martínez & Jairo Hernández Monzón

  2. Fachbereich Mathematik, Universität Konstanz, 78457, Konstanz, Germany

    Robert Denk

Authors
  1. Bienvenido Barraza Martínez
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  2. Robert Denk
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  3. Jairo Hernández Monzón
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Correspondence to Robert Denk.

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Barraza Martínez, B., Denk, R. & Hernández Monzón, J. Pseudodifferential operators with non-regular operator-valued symbols. manuscripta math. 144, 349–372 (2014). https://doi.org/10.1007/s00229-013-0649-3

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  • DOI: https://doi.org/10.1007/s00229-013-0649-3

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