Invertibility of a Volterra operator in a space of analytic functions (Q762747)

Let G be a 1-connected domain in finite complex plane containing the origin, and A(G) be the space of analytic functions in G with the topology of uniform convergence on compacts in G. The general form of an isomorphism of A(G), commuting with any integration operator \[ (If)(z)=\int_{\ell_ z}f(t)dt, \] where \(\ell_ z\) is a Jordan contour in G connecting 0 and z, is obtained in the case when G is a star-like domain.