Geodesic
Pseudodifferential operators on non-quasianalytic classes of Beurling type
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
Studia Mathematica, Tome 167 (2005) no. 2, pp. 99-131 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm167-2-1
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

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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     title = {Pseudodifferential operators on non-quasianalytic classes
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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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