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Currently displaying 1 – 2 of 2

Order by Relevance | Title | Year of publication

A free boundary problem related to single-layer potentials.

Ebenfelt, P.; Khavinson, D.; Shapiro, H. S. — 2002

Annales Academiae Scientiarum Fennicae. Mathematica

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 $f (f \in H^{2})$ , that is, the smallest closed subspace of $H^{2}$ that contains ${U^{* n} f}$ $(n \geq 0)$ . 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 characteristic...

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