Spectrum of the Riemann-Hilbert-Poincaré problem for analytic functions

We study the Riemann-Hilbert-Poincaré boundary value problem for analytic function. This problem will lead to inhomogeneous Fuchsian differential equations. We find that its spectrum is not characterized by the smoothness of its coefficient on the boundary but by its interior analytic continuation p...

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Bibliographic Details
Published in:	Complex variables, theory & application Vol. 50; no. 7-11; pp. 497 - 505
Main Authors:	Dai, Dao-Qing, Liu, Ming-Sheng
Format:	Journal Article
Language:	English
Published:	Taylor & Francis Group 10.06.2005
Subjects:	AMS 2000 Mathematics Subject Classification: 30E25 Analytic function Boundary value problem Inhomogeneous Fuchsian differential equations
ISSN:	0278-1077, 1563-5066
Online Access:	Get full text
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Summary:	We study the Riemann-Hilbert-Poincaré boundary value problem for analytic function. This problem will lead to inhomogeneous Fuchsian differential equations. We find that its spectrum is not characterized by the smoothness of its coefficient on the boundary but by its interior analytic continuation property. Moreover, the multiplicities of eigenfunctions for different eigenvalues are not necessarily the same even when the eigenvalues are small.
ISSN:	0278-1077 1563-5066
DOI:	10.1080/02781070500086552