Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können kommenden Montag und Dienstag keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted next Monday and Tuesday.)
Type of Publication: | Journal article |
Publication status: | Published |
Author: | Barraza Martínez, Bienvenido; Denk, Robert; Hernández Monzón, Jairo; Nau, Tobias |
Year of publication: | 2016 |
Published in: | Journal of Fourier Analysis and Applications ; 22 (2016), 4. - pp. 823-853. - ISSN 1069-5869. - eISSN 1531-5851 |
DOI (citable link): | https://dx.doi.org/10.1007/s00041-015-9437-7 |
Summary: |
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. Here, we restrict ourselves to pseudodifferential operators with x-independent symbols (Fourier multipliers). We show that a parabolic toroidal pseudodifferential operator generates an analytic semigroup on the Besov space Bspq(Tn,E) and on the Sobolev space Wkp(Tn,E), where E is an arbitrary Banach space, 1≤p,q≤∞, s∈R and k∈N0. 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.
|
MSC Classification: | 35S05, 47D06, 35R20 |
Subject (DDC): | 510 Mathematics |
Keywords: | Pseudodifferential operators ; Vector-valued Sobolev spaces ; Toroidal Fourier transform ; Generation of analytic semigroup |
Bibliography of Konstanz: | Yes |
Files | Size | Format | View |
---|---|---|---|
There are no files associated with this item. |
BARRAZA MARTÍNEZ, Bienvenido, Robert DENK, Jairo HERNÁNDEZ MONZÓN, Tobias NAU, 2016. Generation of Semigroups for Vector-Valued Pseudodifferential Operators on the Torus. In: Journal of Fourier Analysis and Applications. 22(4), pp. 823-853. ISSN 1069-5869. eISSN 1531-5851. Available under: doi: 10.1007/s00041-015-9437-7
@article{BarrazaMartinez2016-08Gener-30781, title={Generation of Semigroups for Vector-Valued Pseudodifferential Operators on the Torus}, year={2016}, doi={10.1007/s00041-015-9437-7}, number={4}, volume={22}, issn={1069-5869}, journal={Journal of Fourier Analysis and Applications}, pages={823--853}, author={Barraza Martínez, Bienvenido and Denk, Robert and Hernández Monzón, Jairo and Nau, Tobias} }