Standard deviation and Schatten class Hankel operators on the Segal-Bargmann space

Jingbo Xia; Dechao Zheng

doi:10.1512/iumj.2004.53.2434

Standard deviation and Schatten class Hankel operators on the Segal-Bargmann space

Jingbo Xia
, Dechao Zheng

Mathematics

University at Buffalo

Vanderbilt University

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

24 Scopus citations

Abstract

We consider Hankel operators on the Segal-Bargmann space H ²(ℂⁿ,dμ). Our main result is a necessary and sufficient condition for the simultaneous membership of H_f and H _f in the Schatten class C_p, 1 ≤, p < ∞. We will explain that, since this condition is valid in the case 1 ≤ p ≤ 2 as well as in the case 2 ≤ p < ∞, this result reflects the structural difference between the Segal-Bargmann space and other reproducing-kernel spaces such as the Bergman space L_a²(B_n, dv).

Original language	English
Pages (from-to)	1381-1399
Number of pages	19
Journal	Indiana University Mathematics Journal
Volume	53
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2004.53.2434
State	Published - 2004

Keywords

Hankel operator
Schatten class

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10.1512/iumj.2004.53.2434

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abstract = "We consider Hankel operators on the Segal-Bargmann space H 2(ℂn,dμ). Our main result is a necessary and sufficient condition for the simultaneous membership of Hf and H f in the Schatten class Cp, 1 ≤, p < ∞. We will explain that, since this condition is valid in the case 1 ≤ p ≤ 2 as well as in the case 2 ≤ p < ∞, this result reflects the structural difference between the Segal-Bargmann space and other reproducing-kernel spaces such as the Bergman space La2(Bn, dv).",

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AU - Xia, Jingbo

AU - Zheng, Dechao

PY - 2004

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N2 - We consider Hankel operators on the Segal-Bargmann space H 2(ℂn,dμ). Our main result is a necessary and sufficient condition for the simultaneous membership of Hf and H f in the Schatten class Cp, 1 ≤, p < ∞. We will explain that, since this condition is valid in the case 1 ≤ p ≤ 2 as well as in the case 2 ≤ p < ∞, this result reflects the structural difference between the Segal-Bargmann space and other reproducing-kernel spaces such as the Bergman space La2(Bn, dv).

AB - We consider Hankel operators on the Segal-Bargmann space H 2(ℂn,dμ). Our main result is a necessary and sufficient condition for the simultaneous membership of Hf and H f in the Schatten class Cp, 1 ≤, p < ∞. We will explain that, since this condition is valid in the case 1 ≤ p ≤ 2 as well as in the case 2 ≤ p < ∞, this result reflects the structural difference between the Segal-Bargmann space and other reproducing-kernel spaces such as the Bergman space La2(Bn, dv).

KW - Hankel operator

KW - Schatten class

UR - https://www.scopus.com/pages/publications/11044239398

U2 - 10.1512/iumj.2004.53.2434

DO - 10.1512/iumj.2004.53.2434

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VL - 53

SP - 1381

EP - 1399

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 5

ER -

Standard deviation and Schatten class Hankel operators on the Segal-Bargmann space

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Keywords

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