Kernels of adjoints of composition operators with multivalent symbol via a formal adjoint (Q2478031)

The author gets the description of functions in the kernel of the adjoint of a composition operator \(C_\phi\) defined on the unit \(H^2\) of the unit disc for symbols with variable multiplicity such as \(\phi(z)= \frac{(1-2c)z^2}{1-2cz}\) for \(0<c<1/2\). She shows that, if \(f(0)=0\), then \(f\in\text{Ker}(C_\phi^*)\) if and only if \(\frac{f^{(2j)}(c)}{(2j)!}=c \frac{f^{(2j+1)}(c)}{(2j+1)!}\) for all \(j\). Using this, a formal expression for \(C^*_\phi\) is presented.