Operators commuting with the multiple integration in the space of analytic functions
Let D be a star-shaped (w.r.t. zero) domain in the complex plane. Let \((If)(z)=\int^{z}_{0}f(\zeta)d\zeta\) be the integration operator in the space A(D) of analytic functions on D. Let p be a positive integer. The author describes the commutant of \(I^ p\) in A(D). The results depend on the rotation properties of D. Similar results are obtained for the multiplication operator \((Uf)(z)=zf(z)\).
operator in the space of analytic functions
scientific article; zbMATH DE number 3979835