Hankel operators on planar domains

Jonathan Arazy; Stephen D. Fisher; Jaak Peetre

doi:10.1007/BF01889353

Hankel operators on planar domains

Jonathan Arazy, Stephen D. Fisher, Jaak Peetre

Department of Mathematics

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

Abstract

Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves Let A denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and let P denote the orthogonal projection of L²(Ω, dA) onto A. A function b in A induces a Hankel operator (densely defined) on A by the rule H_b(g)=(I-P)bg. This paper continues earlier investigations of the authors and others by determining conditions under which H_b is bounded, compact, or lies in the Schatten-von Neumann ideal S_p, 1<p<∞

Original language	English
Pages (from-to)	113-138
Number of pages	26
Journal	Constructive Approximation
Volume	6
Issue number	2
DOIs	https://doi.org/10.1007/BF01889353
State	Published - Jun 1990

Keywords

AMS classification: 47B10, 41A35, 46E15
Besov space
Bloch space
Hankel operator
Schatten-von Neumann ideal

ASJC Scopus subject areas

Analysis
General Mathematics
Computational Mathematics

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10.1007/BF01889353

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title = "Hankel operators on planar domains",

abstract = "Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves Let A denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and let P denote the orthogonal projection of L2(Ω, dA) onto A. A function b in A induces a Hankel operator (densely defined) on A by the rule Hb(g)=(I-P)bg. This paper continues earlier investigations of the authors and others by determining conditions under which Hb is bounded, compact, or lies in the Schatten-von Neumann ideal Sp, 1",

keywords = "AMS classification: 47B10, 41A35, 46E15, Besov space, Bloch space, Hankel operator, Schatten-von Neumann ideal",

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doi = "10.1007/BF01889353",

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T1 - Hankel operators on planar domains

AU - Arazy, Jonathan

AU - Fisher, Stephen D.

AU - Peetre, Jaak

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N2 - Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves Let A denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and let P denote the orthogonal projection of L2(Ω, dA) onto A. A function b in A induces a Hankel operator (densely defined) on A by the rule Hb(g)=(I-P)bg. This paper continues earlier investigations of the authors and others by determining conditions under which Hb is bounded, compact, or lies in the Schatten-von Neumann ideal Sp, 1

AB - Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves Let A denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and let P denote the orthogonal projection of L2(Ω, dA) onto A. A function b in A induces a Hankel operator (densely defined) on A by the rule Hb(g)=(I-P)bg. This paper continues earlier investigations of the authors and others by determining conditions under which Hb is bounded, compact, or lies in the Schatten-von Neumann ideal Sp, 1

KW - AMS classification: 47B10, 41A35, 46E15

KW - Besov space

KW - Bloch space

KW - Hankel operator

KW - Schatten-von Neumann ideal

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DO - 10.1007/BF01889353

M3 - Article

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SP - 113

EP - 138

JO - Constructive Approximation

JF - Constructive Approximation

IS - 2

ER -

Hankel operators on planar domains

Abstract

Keywords

ASJC Scopus subject areas

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