On Nontangential Limits and Shift Invariant Subspaces
John R. Akeroyd, John B. Conway, and Liming Yang
TL;DR
This paper reviews solutions and approaches to open questions about shift operators on $P^t(u)$ spaces, highlighting progress and unresolved issues in the field.
Contribution
It summarizes known results, discusses alternative methods, and emphasizes the remaining open problem regarding shift invariant subspaces.
Findings
Some open questions have been fully resolved.
Alternative approaches to the problems are discussed.
At least one key problem remains unsolved.
Abstract
In 1998, John B. Conway and Liming Yang wrote a paper in which they posed a number of open questions regarding the shift on spaces. A few of these have been completely resolved, while at least one remains wide open. In this paper, we review some of the solutions, mention some alternate approaches and discuss further the problem that remains unsolved.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometric Analysis and Curvature Flows · Algebraic and Geometric Analysis