Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-559fc8cf4f-6pznq Total loading time: 0.192 Render date: 2021-03-06T16:07:26.342Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Mathematika Mathematika

Article contents

Toeplitz and Hankel type operators on an annulus

Part of: Special classes of linear operators

Published online by Cambridge University Press:  26 February 2010

Qingtang Jiang  and
Lizhong Peng
Qingtang Jiang
Affiliation:
Institute of Mathematics, Peking University, Beijing 100871, People's Republic of China.
Lizhong Peng
Affiliation:
Institute of Mathematics, Peking University, Beijing 100871, People's Republic of China.
Get access
Rights & Permissions[Opens in a new window]

Extract

Let Ω be a regular domain in the extended complex plane, i.e., it is a bounded domain and its boundary consists of a finite number of disjoint analytic simple closed curves. Let dm(z) be the Lebesgue area measure on Ω and let ds = dm(z)/ω(z) be the Poincare metric on Ω, a Riemannian metric of negative constant curvature. It may be proved that Ω(z) ≈ Euclidean distance from z to the boundary of Ω (see [8]).

MSC classification

Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 266 - 276
Copyright
Copyright © University College London 1994

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

References

1.Arazy, J., Fisher, S. and Peetre, J.. Hankel operators in Bergman spaces. Amer. J. Math., 110 (1988), 989–1053.CrossRefGoogle Scholar
2.Arazy, J., Fisher, S. and Peetre, J.. Hankel operators on planar domains. Constructive Approximation, 6 (1990), 113–138.CrossRefGoogle Scholar
3.Axler, S.. The Bergman kernel, the Bloch space, and commutators of multiplication operators. Duke Math. J., 53 (1986), 315–332.CrossRefGoogle Scholar
4.Gustafsson, B. and Peetre, J.. Hankel forms on multiply connected domains. Part Two. The case of higher connectivity. Complex Variables, 13 (1990), 239–250.Google Scholar
5.Janson, S.. Hankel operators between weighted Bergman spaces. Ark. Math., 26 (1988), 205–219.CrossRefGoogle Scholar
6.Janson, S. and Peetre, J.. Paracommutators-boundedness and Schatten-von Neumann properties. Trans. Amer. Math. Soc., 305 (1988), 467–504.Google Scholar
7.Janson, S., Peetre, J. and Rochberg, R.. Hankel forms and the Fock space. Rev. Mat. Ibero-Amer., 3 (1987), 61–138.CrossRefGoogle Scholar
8.Peetre, J.. Hankel forms on multiply connected plane domains. Complex Variables, 10 (1988), 123–139.Google Scholar
9.Peetre, J. and Zhang, G.. Projective structures on an annulus and Hankel forms. Glasgow Math. J., 33 (1991), 247–266.CrossRefGoogle Scholar
10.Peller, V. V.. Hankel operators of class γp and applications. Math. UssR. Sborrik, 41 (1982), 443–479.CrossRefGoogle Scholar
11.Peng, L.. Paracommutator of Schatten-von Neumann class Sp, O<P<1. Math. Scand., 61 (1987), 68–92.Google Scholar
12.Peng, L.. Toeplitz-Hankel type operators on Bergman space. Mathematika, 40 (1993), 345–356.CrossRefGoogle Scholar
13.Peng, L., Rochberg, R. and Wu, Z.. Laguerre polynomials and Hankel operators on Bergman space. Studia Math., 102 (1992), 57–75.Google Scholar
14.Peng, L. and Xu, C.. Jacobi polynomial and Toeplitz-Hankel type operators. Complex Variables, 22 (1993), 1–25.Google Scholar
15.Peng, L. and Zhang, G.. Middle Hankel operators on Bergman space. In Function Spaces, edited by Jarosz, K., Lecture Notes in Pure and Applied Math., Series 136 (Marcel Dekker, 1991), 225–236.Google Scholar
16.Szegö, G., Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publications, 23 (1939).Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 6 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 6th March 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Toeplitz and Hankel type operators on an annulus
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Toeplitz and Hankel type operators on an annulus
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Toeplitz and Hankel type operators on an annulus
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *