Treffer: UNIFORM ALGEBRAS GENERATED BY HOLOMORPHIC AND CLOSE-TO-HARMONIC FUNCTIONS
Title:
UNIFORM ALGEBRAS GENERATED BY HOLOMORPHIC AND CLOSE-TO-HARMONIC FUNCTIONS
Authors:
Source:
Proceedings of the American Mathematical Society. 139(6):2183-2189
Publisher Information:
Providence, RI: American Mathematical Society, 2011.
Publication Year:
2011
Physical Description:
print, 6 ref
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, Généralités, histoire et biographie, General, history and biography, Mathématiques générales, General mathematics, Algèbre, Algebra, Approximation, Aproximación, Convexité, Convexity, Convexidad, Fonction harmonique, Harmonic function, Función armónica, Fonction holomorphe, Holomorphic function, Función holomorfa, Harmonique, Harmonic, Armónica, Laplacien, Laplacian, Laplaciano, Polynôme, Polynomial, Polinomio, 32Axx, Disque unité, Perturbation faible, Small perturbation, Petite perturbation
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
DEPARTMENT OF MATHEMATICS, INDIAN INSTITUTE OF SCIENCE, BANGALORE ― 560012, India
ISSN:
0002-9939
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
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.24134174
Database:
PASCAL Archive
Weitere Informationen
The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc D generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to ∂D, equals C(D). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is small in a certain sense.