Propagation of Semiclassical Wave Front Sets for Non-Self-Adjoint Matrix-Valued Pseudo-Differential Operators

Yuta Kawamura

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arXiv · 2606.15095

Propagation of Semiclassical Wave Front Sets for Non-Self-Adjoint Matrix-Valued Pseudo-Differential Operators

Yuta Kawamura

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Abstract

We study the semiclassical wave front set of vector-valued microlocal solutions to the pseudo-differential system with a non-Hermitian matrix-valued symbol. The main result establishes the propagation of the semiclassical wave front sets under a generalized microhyperbolicity condition for the real part of the symbol and the non-negativity for the imaginary part. The proof is based on H\"ormander's positive commutator method.

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Yuta Kawamura. 2026-06-13. Propagation of Semiclassical Wave Front Sets for Non-Self-Adjoint Matrix-Valued Pseudo-Differential Operators. https://arxiv.org/abs/2606.15095

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