Pseudodifferential operators on non-quasianalytic classes of Beurling type

Tom 167 / 2005

C. Fernández, A. Galbis, D. Jornet Studia Mathematica 167 (2005), 99-131 MSC: 46F05, 47G30, 35S05, 46E10. DOI: 10.4064/sm167-2-1

Streszczenie

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.

Autorzy

  • C. FernándezDepartamento de Análisis Matemático
    Universidad de Valencia
    Doctor Moliner 50
    46100 Burjasot (Valencia), Spain
    e-mail
  • A. GalbisDepartamento de Análisis Matemático
    Universidad de Valencia
    Doctor Moliner 50
    46100 Burjasot (Valencia), Spain
    e-mail
  • D. JornetDepartamento de Matemática Aplicada
    ETSI Telecomunicación
    Universidad Politécnica de Valencia
    E-46071 Valencia, Spain
    e-mail

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