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

Mikhail Zaidenberg (1)

1 IF - Institut Fourier

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Mikhail Zaidenberg. Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch Theory. Mark Agranovsky et al. Contemporary Mathematics, 554, American Mathematical Society, Bar-Ilan University, pp.265-284, 2011, Complex Analysis and Dynamical Systems IV: General relativity, geometry, and PDE. ⟨hal-00424782v2⟩