Result: TOEPLITZ OPERATORS WITH BMO SYMBOLS ON THE SEGAL-BARGMANN SPACE

Title:
TOEPLITZ OPERATORS WITH BMO SYMBOLS ON THE SEGAL-BARGMANN SPACE
Authors:
COBURN, L. A, ISRALOWITZ, J, BO LI
Source:
Transactions of the American Mathematical Society. 363(6):3015-3030
Publisher Information:
Providence, RI: American Mathematical Society, 2011.
Publication Year:
2011
Physical Description:
print, 1 p
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Analyse fonctionnelle, Functional analysis, Théorie des opérateurs, Operator theory, Généralités, histoire et biographie, General, history and biography, Mathématiques générales, General mathematics, Analyse Fourier, Fourier analysis, Análisis Fourier, Compacité, Compactness, Compacidad, Contre exemple, Counterexample, Contraejemplo, Espace Sobolev, Sobolev space, Espacio Sobolev, Isométrie, Isometry, Isometría, Localisation, Localization, Localización, Opérateur Toeplitz, Toeplitz operator, Operador Toeplitz, Opérateur borné, Bounded operator, Operador acotado, Opérateur compact, Compact operator, Operador compacto, 32A36, 46E35, 47B35, Disque unité, Espace Bergman, Fonction carré sommable, Square integrable function
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
DEPARTMENT OF MATHEMATICS, SUNY AT BUFFALO, BUFFALO, NEW YORK 14260, United States
ISSN:
0002-9947
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=24147240
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24147240
Database:
PASCAL Archive

Further Information

We show that Zorboska's criterion for compactness of Toeplitz operators with BMO1 symbols on the Bergman space of the unit disc holds, by a different proof, for the Segal-Bargmann space of Gaussian square-integrable entire functions on ℂn. We establish some basic properties of BMOTp for p > 1 and complete the characterization of bounded and compact Toeplitz operators with BMO1 symbols. Via the Bargmann isometry and results of Lo and Englis, we also give a compactness criterion for the Gabor-Daubechies windowed Fourier localization operators on L2 (ℝn, dv) when the symbol is in a BMO1 Sobolev-type space. Finally, we discuss examples of the compactness criterion and counterexamples to the unrestricted application of this criterion for the compactness of Toeplitz operators.