Quantizations and Global Hypoellipticity for Pseudodifferential Operators of Infinite Order in Classes of Ultradifferentiable Functions

Asensio, Vicente

doi:10.1007/s00009-022-02034-1

Cited by 2 publications

(1 citation statement)

References 25 publications

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“…See [10,11] for wave front sets of Gel'fand-Shilov type. Recently, the author, Boiti, Jornet, and Oliaro [2], using the theory developed in [1], generalized the concept of C ∞ wave front set to spaces of ω-tempered ultradistributions following the ideas given in [20,26], and provided conditions on the weight function under which this wave front set and the analytic wave front set in [7] are equal.…”

Section: Introductionmentioning

confidence: 99%

The Wigner global wave front set in spaces of tempered ultradistributions

Asensio

2023

J. Pseudo-Differ. Oper. Appl.

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In this paper we introduce and study global wave front sets in terms of the $$\tau $$ τ -Wigner transform in global ultradifferentiable classes of Beurling type modulated with weight functions in the sense of Braun, Meise, and Taylor, and we compare it with other wave front sets existing in the literature defined by different time-frequency analysis tools, such as the short-time Fourier transform or Gabor frames. Conditions for the equality of these wave front sets are provided and some examples are given.

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Section: Introductionmentioning

confidence: 99%

The Wigner global wave front set in spaces of tempered ultradistributions

Asensio

2023

J. Pseudo-Differ. Oper. Appl.

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Almost diagonalization theorem and global wave front sets in ultradifferentiable classes

Asensio

2024

Banach J. Math. Anal.

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The main aim of this paper is to prove that the wave front set of $$a^w(x,D)u$$ a w ( x , D ) u , i.e. the action of the Weyl operator with symbol a on u, is contained in the wave front set of u and in the conic support of a in spaces of $$\omega $$ ω -tempered ultradistributions in the Beurling setting for adequate symbols of ultradifferentiable type. These symbols are not restricted to have order zero. To do so, we prove an almost diagonalization theorem on Weyl operators. Furthermore, an almost diagonalization theorem involving time-frequency analysis leads to additional applications, such as invertibility of pseudodifferential operators or boundedness of them in modulation spaces with exponential growth.

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Quantizations and Global Hypoellipticity for Pseudodifferential Operators of Infinite Order in Classes of Ultradifferentiable Functions

Cited by 2 publications

References 25 publications

The Wigner global wave front set in spaces of tempered ultradistributions

The Wigner global wave front set in spaces of tempered ultradistributions

Almost diagonalization theorem and global wave front sets in ultradifferentiable classes

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