1Departamento de Análisis Matemático Universidad de Valencia Doctor Moliner 50 46100 Burjasot (Valencia), Spain 2Departamento de Matemática Aplicada ETSI Telecomunicación Universidad Politécnica de Valencia E-46071 Valencia, Spain
Studia Mathematica, Tome 167 (2005) no. 2, pp. 99-131
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
1
Departamento de Análisis Matemático Universidad de Valencia Doctor Moliner 50 46100 Burjasot (Valencia), Spain
2
Departamento de Matemática Aplicada ETSI Telecomunicación Universidad Politécnica de Valencia E-46071 Valencia, Spain
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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},
year = {2005},
volume = {167},
number = {2},
doi = {10.4064/sm167-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm167-2-1/}
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AU - A. Galbis
AU - D. Jornet
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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
