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arXiv · 2607.03507

The Oracle Theorem for Matrix-Valued Jacobi Operators

Silas L. Carvalho·Douglas C. P. Freitas
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Abstract

This paper develops the matrix-valued analogue of the reflectionless and oracle framework for Jacobi operators. Starting from matrix-valued Weyl--Titchmarsh $m$-functions on the Siegel upper half-space, we study the distance-decreasing action of transfer matrices, matrix-valued harmonic measures and value distribution convergence. These ingredients are then used to establish the reflectionless property of the $\omega$-limit set and to prove an Oracle Theorem for matrix-valued Jacobi operators with absolutely continuous spectrum of full multiplicity.

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Silas L. Carvalho, Douglas C. P. Freitas. 2026-07-03. The Oracle Theorem for Matrix-Valued Jacobi Operators. https://arxiv.org/abs/2607.03507

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