Characterizations of a class of Pilipovi{ć} spaces by powers of harmonic oscillator

Ahmed Abdeljawad, Carmen Fernandez, Antonio Galbis +2

We show that a smooth function $f$ on ${\mathbf{R}}^d$ belongs to the Pilipovi{ć} space ${\mathcal{H}}_{{♭}_{\sigma }}({\mathbf{R}}^d)$ or the Pilipovi{ć} space $\mathcal H_{0,\flat _σ}(\mathbf…