Smooth Functions in Star-invariant Subspaces

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

Bad boundary behavior in star invariant subspaces I

We discuss the boundary behavior of functions in star invariant subspaces (BH2)⊥, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.

Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

Bad Boundary Behavior in Star Invariant Subspaces II

We continue our study begun in [HR11] concerning the radial growth of functions in the model spaces (IH).

Extending Functions in the Model Subspaces of H^2(R) to C