On spectral expansions of functions of the Nikol'skiĭ class (Q2583649)

The author considers the operator obtained by functional composition \(p(tA)\), where \(A\) is a positive selfadjoint classical pseudodifferential operator, and \(t\in\mathbb{R}\). Under suitable assumptions on the function \(p(z)\), the composition \(p(tA)\) can be defined in terms of the Neumann spectral theorem. The author proves results of continuity of \(p(tA)\) on the function spaces of \textit{S. M. Nikol'skiĭ} [Approximation of functions of several variables and embedding theorems (Moskva: Nauka) (1977; Zbl 0496.46020)].