On Spectrum of a Selfadjoint Difference Operator on the Graph-Tree

We consider a class of the selfadjoint discrete Schrödinger operators defined on an infinite homogeneous rooted graph-tree. The potential of this operator consists of the coefficients of the Nearest Neighbor Recurrence Relations (NNRRs) for the Multiple Orthogonal Polynomials (MOPs).
For the general class of potentials, generated by Angelesco MOPs we prove that the essential spectrum of these operators is a union of the supports of the components of the vector orthogonality measure $\vec{\mu}:=(\mu_{1},\ldots,\mu_{d})$ for the Angelesco MOPs. It is a joint work with Sergey Denisov (Madison University) and Maxim Yattselev (IUPUI).