Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch Theory
Analysis of PDEs
2010-06-01 v2 Mathematical Physics
math.MP
Abstract
The classical Floquet theory deals with Floquet-Bloch solutions of periodic PDEs (see e.g., P. Kuchment. Floquet Theory for Partial Differential Equations. Basel: Birkhauser, 1993). Peter Kuchment developed as well a discrete version of this theory for difference vector equations on lattices, including the Floquet theory on infinite periodic graphs. Here we propose a variation on this theory for matrix convolution operators acting on vector functions on lattices with values in a field of positive characteristic.
Keywords
Cite
@article{arxiv.0910.3351,
title = {Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch Theory},
author = {Mikhail Zaidenberg},
journal= {arXiv preprint arXiv:0910.3351},
year = {2010}
}