Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms

Abstract

We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform. In particular, we obtain some results of regularity in the Schwartz space $\mathcal{S}$ and in the space ${\mathcal{S}}_{\omega }$ as introduced by Björck for weight functions $\omega$. Several examples are discussed in this new setting.

References in corpus (1)

• Regularity of class of differential operators

Cited by in corpus (7)

• Real Paley-Wiener theorems in spaces of ultradifferentiable functions
• Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions
• About the nuclearity of ${\mathcal{S}}_{(M_p)}$ and ${\mathcal{S}}_{\omega }$
• Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis
• Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
• The Overdetermined Cauchy Problem for $\omega$-ultradifferentiable Functions
• Mean-dispersion principles and the Wigner transform