Spectrum of analytic continuation

2008/06/03 by David V. Ingerman, Ingerman, David V.
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Holomorphic and Operator Theory #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.0806.0655

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.

Citations

• Circular planar graphs and resistor networks

Related

• Graphs with positive spectrum
• On the Landis Conjecture for Positive Quasi-linear Operators on Graphs
• Some Spectral Properties of the B_α Matrix of a Graph
• Invariant graphs and spectral type of Schrödinger operators
• Eigenvalue asymptotics and unique continuation of eigenfunctions on planar graphs