Operators commuting with multiplication in spaces of analytic functions of one variable

V. P. Zakharyuta ; M. Yu. Tsar'kov

Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 269-276.

Résumé

Let $D$ be an analytic manifold of dimensionality $\mathfrak A(D)$ be the space of functions analytic on $D$ with the topology of compact convergence, and $\varphi(z)$ be a function from $\mathfrak A(D)$. Under certain sufficiently general assumptions relative to the manifold $D$, in the note is found the general form of a continuous linear operator $\mathfrak A(D)$, commuting with the operator of multiplication by a function $\varphi(z)$. Because of this it is established under what conditions each such operator is an operator of multiplication by some function.