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Lookup NU author(s): Professor Mihai Putinar
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors–Beurling transform acting on the associated Bergman space. Consequently, the similarity equivalence between the Ahlfors–Beurling transform and the Neumann–Poincaré operator provides the spectrum of the latter integral operator on a wedge. A localization technique and conformal mapping lead to the first complete description of the essential spectrum of the Neumann–Poincaré operator on a planar domain with corners, with respect to the energy norm of the associated harmonic field.
Author(s): Perfekt KM, Putinar M
Publication type: Article
Publication status: Published
Journal: Archive for Rational Mechanics and Analysis
Year: 2017
Volume: 223
Issue: 2
Pages: 1019-1033
Print publication date: 01/02/2017
Online publication date: 31/10/2016
Acceptance date: 22/09/2016
Date deposited: 07/11/2016
ISSN (print): 0003-9527
ISSN (electronic): 1432-0673
Publisher: Springer
URL: http://dx.doi.org/10.1007/s00205-016-1051-6
DOI: 10.1007/s00205-016-1051-6
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