The existence of a point spectral radius for pseudodifferential operators
Let \(M_{K \varphi}\) denote the Orlicz space defined by a Young function \(\Phi\), whose elements \(f\) have the property that \(\text{supp} \widehat f\subset K\), \(K\) a compact set in \(\mathbb{R}^n\). The author introduces an algebra of \(\psi DO\) such that for any element \(A(D)\) of this algebra there always exists the limit \(\lim_{m\to \infty} \| A^m(D)f \|^{1/m}\) for any \(f\in M_{K \varphi}\), where \(\| \cdot \|\) denotes the norm in \(M_{K \varphi}\). The spectral radius of the \(\psi DO\) of the introduced algebra is evaluated and, as applications, some convex and non-convex versions of the Paley-Wiener theorem are obtained.
scientific article; zbMATH DE number 1122789
scientific article