Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch Theory

Details Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch Theory Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch Theory

2009-10-18

arxiv.org/abs/0910.3351v2

Mathematics

Analysis of PDEs

Scientific paper

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.

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