The Helton-Howe trace formula for submodules

Quanlei Fang; Yi Wang; Jingbo Xia

doi:10.1016/j.jfa.2021.108997

The Helton-Howe trace formula for submodules

Quanlei Fang
, Yi Wang
, Jingbo Xia

Mathematics

City University of New York
SUNY Buffalo

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

4 Scopus citations

Abstract

We consider a class of submodules R of the Bergman module L_a²(B) that are associated with analytic sets M˜⊂Cⁿ with dim_CM˜=d. In analogue to the usual Toeplitz operator on L_a²(B), we have the “Toeplitz operator for the submodule” R_φ on R. We show that the Helton-Howe trace formula holds for the antisymmetric sum [R_f₁,R_f₂,…,R_{f_2n}], f₁,f₂,…,f_2n ∈ C[z₁,z¯₁,…,z_n,z¯_n].

Original language	English
Article number	108997
Journal	Journal of Functional Analysis
Volume	281
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2021.108997
State	Published - Jul 1 2021

Keywords

Antisymmetric sum
Submodule
Trace formula

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10.1016/j.jfa.2021.108997

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title = "The Helton-Howe trace formula for submodules",

abstract = "We consider a class of submodules R of the Bergman module La2(B) that are associated with analytic sets M˜⊂Cn with dimCM˜=d. In analogue to the usual Toeplitz operator on La2(B), we have the “Toeplitz operator for the submodule” Rφ on R. We show that the Helton-Howe trace formula holds for the antisymmetric sum [Rf1,Rf2,…,Rf2n], f1,f2,…,f2n ∈ C[z1,z¯1,…,zn,z¯n].",

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author = "Quanlei Fang and Yi Wang and Jingbo Xia",

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AU - Fang, Quanlei

AU - Wang, Yi

AU - Xia, Jingbo

PY - 2021/7/1

Y1 - 2021/7/1

N2 - We consider a class of submodules R of the Bergman module La2(B) that are associated with analytic sets M˜⊂Cn with dimCM˜=d. In analogue to the usual Toeplitz operator on La2(B), we have the “Toeplitz operator for the submodule” Rφ on R. We show that the Helton-Howe trace formula holds for the antisymmetric sum [Rf1,Rf2,…,Rf2n], f1,f2,…,f2n ∈ C[z1,z¯1,…,zn,z¯n].

AB - We consider a class of submodules R of the Bergman module La2(B) that are associated with analytic sets M˜⊂Cn with dimCM˜=d. In analogue to the usual Toeplitz operator on La2(B), we have the “Toeplitz operator for the submodule” Rφ on R. We show that the Helton-Howe trace formula holds for the antisymmetric sum [Rf1,Rf2,…,Rf2n], f1,f2,…,f2n ∈ C[z1,z¯1,…,zn,z¯n].

KW - Antisymmetric sum

KW - Submodule

KW - Trace formula

UR - https://www.scopus.com/pages/publications/85103326706

U2 - 10.1016/j.jfa.2021.108997

DO - 10.1016/j.jfa.2021.108997

M3 - Article

AN - SCOPUS:85103326706

SN - 0022-1236

VL - 281

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

M1 - 108997

ER -

The Helton-Howe trace formula for submodules

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Keywords

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