Spectrum of analytic continuation
David V. Ingerman
TL;DR
This paper demonstrates that the operator for harmonic analytic continuation on a lattice graph has a positive spectrum, using properties of totally positive matrices, and conjectures similar results for continuous cases.
Contribution
It introduces a positivity result for the spectrum of the harmonic continuation operator on lattice graphs and conjectures its extension to continuous planes.
Findings
Operator has a positive spectrum on lattice graphs
Uses theorem on totally positive matrices
Conjectures extension to continuous plane
Abstract
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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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Holomorphic and Operator Theory · Matrix Theory and Algorithms