Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2017-01-01

Journal: NEW YORK JOURNAL OF MATHEMATICS

Included Journals: Scopus、SCIE

Volume: 23

Page Number: 505-526

ISSN: 1076-9803

Key Words: Hardy space over the bidisk; submodule; core operator; fringe operator; Toeplitz matrix

Abstract: The Hardy space H-2(D-2) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H-2(D-2), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes these invariants for homogeneous submodules through Toeplitz determinants.