Pseudodifferential operators with non-regular operator-valued symbols

Type of Publication: Journal article
Author: Martinez, Bienvenido Barraza; Denk, Robert; Monzon, Jairo Hernandez
Year of publication: 2014
Published in: Manuscripta Mathematica ; 144 (2014), 3-4. - pp. 349-372. - ISSN 0025-2611. - eISSN 1432-1785
DOI (citable link): https://dx.doi.org/10.1007/s00229-013-0649-3
Summary:
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.
Subject (DDC): 510 Mathematics
Keywords: Mathematics, general, Algebraic Geometry, Topological Groups, Lie Groups, Geometry, Number Theory, Calculus of Variations and Optimal Control, Optimization
Bibliography of Konstanz: Yes

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MARTINEZ, Bienvenido Barraza, Robert DENK, Jairo Hernandez MONZON, 2014. Pseudodifferential operators with non-regular operator-valued symbols. In: Manuscripta Mathematica. 144(3-4), pp. 349-372. ISSN 0025-2611. eISSN 1432-1785. Available under: doi: 10.1007/s00229-013-0649-3

@article{Martinez2014Pseud-29174, title={Pseudodifferential operators with non-regular operator-valued symbols}, year={2014}, doi={10.1007/s00229-013-0649-3}, 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} }

Martinez, Bienvenido Barraza 2014-10-23T12:07:14Z eng Pseudodifferential operators with non-regular operator-valued symbols Martinez, Bienvenido Barraza Denk, Robert 2014-10-23T12:07:14Z Denk, Robert Monzon, Jairo Hernandez Monzon, Jairo Hernandez 2014 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<sup>k</sup><sub>p</sub>(R<sup>n</sup>,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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