Pseudodifferential operators on non-quasianalytic classes
of Beurling type
Studia Mathematica, Tome 167 (2005) no. 2, pp. 99-131
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We introduce pseudodifferential operators (of
infinite order) in the framework of non-quasianalytic classes of
Beurling type. We prove that such an operator with
(distributional) kernel in a given Beurling class ${\mathcal
D}'_{(\omega)}$ is pseudo-local and can be locally decomposed,
modulo a smoothing operator, as the composition of a
pseudodifferential operator of finite order and an
ultradifferential operator with constant coefficients in the sense
of Komatsu, both operators with kernel in the same class ${\mathcal
D}'_{(\omega)}$. We also develop the corresponding symbolic
calculus.
Keywords:
introduce pseudodifferential operators infinite order framework non quasianalytic classes beurling type prove operator distributional kernel given beurling class mathcal omega pseudo local locally decomposed modulo smoothing operator composition pseudodifferential operator finite order ultradifferential operator constant coefficients sense komatsu operators kernel class mathcal omega develop corresponding symbolic calculus
Affiliations des auteurs :
C. Fernández 1 ; A. Galbis 1 ; D. Jornet 2
@article{10_4064_sm167_2_1,
author = {C. Fern\'andez and A. Galbis and D. Jornet},
title = {Pseudodifferential operators on non-quasianalytic classes
of {Beurling} type},
journal = {Studia Mathematica},
pages = {99--131},
publisher = {mathdoc},
volume = {167},
number = {2},
year = {2005},
doi = {10.4064/sm167-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm167-2-1/}
}
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C. Fernández; A. Galbis; D. Jornet. Pseudodifferential operators on non-quasianalytic classes of Beurling type. Studia Mathematica, Tome 167 (2005) no. 2, pp. 99-131. doi: 10.4064/sm167-2-1
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