Spectrum of analytic continuation

I will show that operator of analytic (harmonic) continuation on a lattice graph has a positive spectrum. I use a theorem about positivity of eigenvalues of totally positive matrices. I conjecture that by approximation the similar result holds in continuous case on a plane.

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Bibliographic Details
Published in:arXiv.org 2008-06
Main Author: Ingerman, David V
Format: Article
Language:English
Subjects:
Eigenvalues
Mathematical analysis
Operators (mathematics)
Online Access:Get full text
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Summary:I will show that operator of analytic (harmonic) continuation on a lattice graph has a positive spectrum. I use a theorem about positivity of eigenvalues of totally positive matrices. I conjecture that by approximation the similar result holds in continuous case on a plane.
ISSN:2331-8422