2012/05/20 by Niteesh Sahni, Sahni, Niteesh, Dinesh Singh +1
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.FA
paper · pdf · doi:10.48550/arxiv.1205.4394
14 pages
openalex publication_date 2012/05/20 · arxiv created 2012/07/31 · arxiv updated 2012/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we characterize for 0 < p ≤ ∞, the closed subspaces of Hp that are invariant under multiplication by all powers of a finite Blaschke factor B, except the first power. Our result clearly generalizes the invariant subspace theorem obtained by Paulsen and Singh [9] which has proved to be the starting point of important work on constrained Nevanlinna-Pick interpolation. Our method of proof can also be readily adapted to the case where the subspace is invariant under all positive powers of B (z). The two results are in the mould of the classical Lax-Halmos Theorem and can be said to be Lax-Halmos type results in the finitre multiplicity case for two commuting shifts and for a single shift respectively.