2013/04/04 by Jaydeb Sarkar, Sarkar, Jaydeb · 1 citation
Mathematics · #30H10 #46E20 #47A13 #47A15 #47A20 #47A45 #47A80 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1304.1564
openalex publication_date 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We say that a submodule \cls of H2(\mathbbDn) (n >1) is co-doubly commuting if the quotient module H2(\mathbbDn)/\cls is doubly commuting. We show that a co-doubly commuting submodule of H2(\mathbbDn) is essentially doubly commuting if and only if the corresponding one variable inner functions are finite Blaschke products or that n = 2. In particular, a co-doubly commuting submodule \cls of H2(\mathbbDn) is essentially doubly commuting if and only if n = 2 or that \cls is of finite co-dimension. We obtain an explicit representation of the Beurling-Lax-Halmos inner functions for those submodules of H2_H2(\mathbbDn-1)(\mathbbD) which are co-doubly commuting submodules of H2(\mathbbDn). Finally, we prove that a pair of co-doubly commuting submodules of H2(\mathbbDn) are unitarily equivalent if and only if they are equal.