# 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} }

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.

## 6 Citations

Quantizations and global hypoellipticity for pseudodifferential operators of infinite order in classes of ultradifferentiable functions

- Mathematics
- 2021

We study the change of quantization for a class of global pseudodifferential operators of infinite order in the setting of ultradifferentiable functions of Beurling type. The composition of different…

Time-periodic Gelfand-Shilov spaces and global hypoellipticity on $\mathbb{T} \times \mathbb{R}^n$

- Mathematics
- 2021

We introduce a class of time-periodic Gelfand-Shilov spaces of functions on T×R, where T ∼ R/2πZ is the one-dimensional torus. We develop a Fourier analysis inspired by the characterization of the…

The Theorem of Iterates for elliptic and non-elliptic Operators

- Mathematics
- 2021

We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the…

Time-periodic Gelfand-Shilov spaces and global hypoellipticity on TRn

- 2021

We introduce a class of time-periodic Gelfand-Shilov spaces of functions on T×R, where T ∼ R/2πZ is the one-dimensional torus. We develop a Fourier analysis inspired by the characterization of the…

Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

- Mathematics
- 2019

We use techniques from time-frequency analysis to show that the space $${\mathcal{S}}_\omega$$ S ω of rapidly decreasing $$\omega$$ ω -ultradifferentiable functions is nuclear for every weight…

Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting

- Medicine, MathematicsBanach journal of mathematical analysis
- 2021

We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the…

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