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 Bj\"orck for weight functions $\omega$. Several examples are discussed in this new setting.
Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms
OLIARO, Alessandro
2017-01-01
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 Bj\"orck for weight functions $\omega$. Several examples are discussed in this new setting.
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