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arXiv · 1504.04473

Generation of semigroups for vector-valued pseudodifferential operators on the torus

Bienvenido Barraza Martinez·Robert Denk·Jairo Hernandez Monzon·Tobias Nau
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Abstract

We consider toroidal pseudodifferential operators with operator-valued symbols, their mapping properties and the generation of analytic semigroups on vector-valued Besov and Sobolev spaces. We show that a parabolic toroiodal pseudodifferential operator generates an analytic semigroup both on Banach space-valued Besov spaces and on Banach space-valued Sobolev spaces. Here, no condition on the Banach space is imposed. For the proof of the Sobolev space result, we establish a uniform estimate on the kernel which is given as an infinite parameter-dependent sum. An application to abstract non-autonomous periodic pseudodifferential Cauchy problems gives the existence and uniqueness of classical solutions for such problems.

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Bienvenido Barraza Martinez, Robert Denk, Jairo Hernandez Monzon, Tobias Nau. 2015-04-17. Generation of semigroups for vector-valued pseudodifferential operators on the torus. https://arxiv.org/abs/1504.04473

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