Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions

@article{Asensio2019GlobalPO,
  title={Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions},
  author={Vicente Asensio and David Jornet},
  journal={Revista de la Real Academia de Ciencias Exactas, F{\'i}sicas y Naturales. Serie A. Matem{\'a}ticas},
  year={2019}
}
  • Vicente Asensio, D. Jornet
  • Published 6 February 2019
  • Mathematics
  • Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
We develop a theory of pseudodifferential operators of infinite order for the global classes $\mathcal{S}_{\omega}$ of ultradifferentiable functions in the sense of Bj\"orck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of Komatsu. We study the composition and the transpose of such operators with symbolic calculus and provide several examples. 
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