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arXiv · 2512.22547

The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators

Horia D. Cornean·Bernard Helffer·Radu Purice
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Abstract

We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen as operators on the $d$-dimensional torus, and also when they are seen as infinite matrices acting on a discrete $\ell^2$ space via a discrete Fourier transform. Moreover, using these distribution kernels we prove that the fibre operators are toroidal pseudo-differential operators.

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Horia D. Cornean, Bernard Helffer, Radu Purice. 2025-12-27. The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators. https://doi.org/10.1007/s11868-026-00788-w

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