Quotient Hardy modules

Ronald G. Douglas; Rongwei Yang

Quotient Hardy modules

Ronald G. Douglas
, Rongwei Yang

Mathematics and Statistics

University at Albany

Texas A&M University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Suppose H²(Dⁿ) is the Hardy space over the unit polydisk Dⁿ, and [h] is the closed submodule generated by a function h ∈ H^∞(Dⁿ). The quotient H₂(Dⁿ) ⊖ [h] is an A(Dⁿ) module and the coordinate functions z₁, z₂, ..., z_n act on H²(Dⁿ) ⊖ [h] as bounded linear operators. In this paper, we first make a study of the spectral properties of these operators and reveal how these properties are related to the function h. Then we will have a look at the analytic continuation problem. At last, we will show a rigidity phenomenon of quotient Hardy modules.

Original language	English
Pages (from-to)	507-517
Number of pages	11
Journal	Houston Journal of Mathematics
Volume	24
Issue number	3
State	Published - 1998

Cite this

@article{35947ed2d04849ab9d0d87ba568687f5,

title = "Quotient Hardy modules",

abstract = "Suppose H2(Dn) is the Hardy space over the unit polydisk Dn, and [h] is the closed submodule generated by a function h ∈ H∞(Dn). The quotient H2(Dn) ⊖ [h] is an A(Dn) module and the coordinate functions z1, z2, ..., zn act on H2(Dn) ⊖ [h] as bounded linear operators. In this paper, we first make a study of the spectral properties of these operators and reveal how these properties are related to the function h. Then we will have a look at the analytic continuation problem. At last, we will show a rigidity phenomenon of quotient Hardy modules.",

author = "Douglas, \{Ronald G.\} and Rongwei Yang",

year = "1998",

language = "English",

volume = "24",

pages = "507--517",

journal = "Houston Journal of Mathematics",

issn = "0362-1588",

publisher = "University of Houston",

number = "3",

}

TY - JOUR

T1 - Quotient Hardy modules

AU - Douglas, Ronald G.

AU - Yang, Rongwei

PY - 1998

Y1 - 1998

N2 - Suppose H2(Dn) is the Hardy space over the unit polydisk Dn, and [h] is the closed submodule generated by a function h ∈ H∞(Dn). The quotient H2(Dn) ⊖ [h] is an A(Dn) module and the coordinate functions z1, z2, ..., zn act on H2(Dn) ⊖ [h] as bounded linear operators. In this paper, we first make a study of the spectral properties of these operators and reveal how these properties are related to the function h. Then we will have a look at the analytic continuation problem. At last, we will show a rigidity phenomenon of quotient Hardy modules.

AB - Suppose H2(Dn) is the Hardy space over the unit polydisk Dn, and [h] is the closed submodule generated by a function h ∈ H∞(Dn). The quotient H2(Dn) ⊖ [h] is an A(Dn) module and the coordinate functions z1, z2, ..., zn act on H2(Dn) ⊖ [h] as bounded linear operators. In this paper, we first make a study of the spectral properties of these operators and reveal how these properties are related to the function h. Then we will have a look at the analytic continuation problem. At last, we will show a rigidity phenomenon of quotient Hardy modules.

UR - https://www.scopus.com/pages/publications/0032441624

M3 - Article

SN - 0362-1588

VL - 24

SP - 507

EP - 517

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

IS - 3

ER -

Quotient Hardy modules

Abstract

Other files and links

Fingerprint

Cite this