Geodesic
Discrete Schr\"odinger Operator on a Tree, Angelesco Potentials, and Their Perturbations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 5-13

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a class of discrete Schrödinger operators on an infinite homogeneous rooted tree. Potentials for these operators are given by the coefficients of recurrence relations satisfied on a multidimensional lattice by multiple orthogonal polynomials. For operators on a binary tree with potentials generated by multiple orthogonal polynomials with respect to systems of measures supported on disjoint intervals (Angelesco systems) and for compact perturbations of such operators, we show that the essential spectrum is equal to the union of the intervals supporting the orthogonality measures. 
@article{TM_2020_311_a0,
     author = {A. I. Aptekarev and S. A. Denisov and M. L. Yattselev},
     title = {Discrete {Schr\"odinger} {Operator} on a {Tree,} {Angelesco} {Potentials,} and {Their} {Perturbations}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {5--13},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_311_a0/}
}
TY  - JOUR
AU  - A. I. Aptekarev
AU  - S. A. Denisov
AU  - M. L. Yattselev
TI  - Discrete Schr\"odinger Operator on a Tree, Angelesco Potentials, and Their Perturbations
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2020
SP  - 5
EP  - 13
VL  - 311
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2020_311_a0/
LA  - ru
ID  - TM_2020_311_a0
ER  - 
%0 Journal Article
%A A. I. Aptekarev
%A S. A. Denisov
%A M. L. Yattselev
%T Discrete Schr\"odinger Operator on a Tree, Angelesco Potentials, and Their Perturbations
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2020
%P 5-13
%V 311
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2020_311_a0/
%G ru
%F TM_2020_311_a0
A. I. Aptekarev; S. A. Denisov; M. L. Yattselev. Discrete Schr\"odinger Operator on a Tree, Angelesco Potentials, and Their Perturbations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 5-13. http://geodesic.mathdoc.fr/item/TM_2020_311_a0/