Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory

The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner functions, conservative discrete-time input/state/output linear systems, and $C_{\cdot 0}$ Hilbert-space contraction operators. We discuss an analogue of all these ideas in the context of weighted Hardy spaces over the unit disk and an associated class of hypercontraction operators

On the Approximation of Isolated Eigenvalues of Ordinary Differential Operators

We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.Comment: 4 page