The Oracle Theorem for Matrix-Valued Jacobi Operators

Silas L. Carvalho; Douglas C. P. Freitas

The Oracle Theorem for Matrix-Valued Jacobi Operators

数学物理 2026-07-03 v1

作者: Silas L. Carvalho , Douglas C. P. Freitas

摘要

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.

引用

@article{arxiv.2607.03507,
  title  = {The Oracle Theorem for Matrix-Valued Jacobi Operators},
  author = {Silas L. Carvalho and Douglas C. P. Freitas},
  journal= {arXiv preprint arXiv:2607.03507},
  year   = {2026}
}