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.
Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms
BOITI, Chiara;Oliaro, Alessandro
2017
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.File in questo prodotto:
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