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Pseudodifferential operators with non-regular operator-valued symbols

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2014

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Martinez, Bienvenido Barraza
Monzon, Jairo Hernandez

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https://doi.org/10.1007/s00229-013-0649-3
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Manuscripta Mathematica. 2014, 144(3-4), pp. 349-372. ISSN 0025-2611. eISSN 1432-1785. Available under: doi: 10.1007/s00229-013-0649-3

Zusammenfassung

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 Wkp(Rn,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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510 Mathematik

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Mathematics, general, Algebraic Geometry, Topological Groups, Lie Groups, Geometry, Number Theory, Calculus of Variations and Optimal Control, Optimization

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ISO 690MARTINEZ, Bienvenido Barraza, Robert DENK, Jairo Hernandez MONZON, 2014. Pseudodifferential operators with non-regular operator-valued symbols. In: Manuscripta Mathematica. 2014, 144(3-4), pp. 349-372. ISSN 0025-2611. eISSN 1432-1785. Available under: doi: 10.1007/s00229-013-0649-3
BibTex
@article{Martinez2014Pseud-29174,
  year={2014},
  doi={10.1007/s00229-013-0649-3},
  title={Pseudodifferential operators with non-regular operator-valued symbols},
  number={3-4},
  volume={144},
  issn={0025-2611},
  journal={Manuscripta Mathematica},
  pages={349--372},
  author={Martinez, Bienvenido Barraza and Denk, Robert and Monzon, Jairo Hernandez}
}
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