Displaying similar documents to “The geometry of the period mapping on cyclic covers of P1”

Cyclic vectors and invariant subspaces for the backward shift operator

R. G. Douglas, H. S. Shapiro, A. L. Shields (1970)

Annales de l'institut Fourier


The operator U of multiplication by z on the Hardy space H 2 of square summable power series has been studied by many authors. In this paper we make a similar study of the adjoint operator U * (the “backward shift”). Let K f denote the cyclic subspace generated by f ( f H 2 ) , that is, the smallest closed subspace of H 2 that contains { U * n f } ( n 0 ) . If K f = H 2 , then f is called a cyclic vector for U * . Theorem : f is a cyclic vector if and only if there is a function g , meromorphic and of bounded Nevanlinna...