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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 311, Pages 5–13
DOI: https://doi.org/10.4213/tm4124 (Mi tm4124) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Discrete Schrödinger Operator on a Tree, Angelesco Potentials, and Their Perturbations

A. I. Aptekareva, S. A. Denisovba, M. L. Yattselevca

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia
b Department of Mathematics, University of Wisconsin–Madison, 480n Lincoln Dr., Madison, WI 53706, USA
c Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, 402 N. Blackford Str., Indianapolis, IN 46202, USA
Full-text PDF (221 kB) Citations (7)
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DOI: https://doi.org/10.4213/tm4124
Abstract: 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.
Funding agency Grant number
Russian Science Foundation 19-71-30004
Moscow Center of Fundamental and Applied Mathematics 20-03-01
National Science Foundation DMS-1464479
DMS-1764245
Simons Foundation CGM-354538
Van Vleck Professorship Research Award
The work of the first author (Sections 1 and 2) was supported the Russian Science Foundation under grant 19-71-30004. The work of the second and third authors (Section 3) was supported by the Moscow Center for Fundamental and Applied Mathematics (project no. 20-03-01). The second author was also supported by the National Science Foundation (grants DMS-1464479 and DMS-1764245) and by the Van Vleck Professorship Research Award. The third author was also supported by the Simons Foundation (grant CGM-354538).
Received: April 20, 2020
Revised: May 16, 2020
Accepted: June 29, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 311, Pages 1–9
DOI: https://doi.org/10.1134/S0081543820060012
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Discrete Schrödinger Operator on a Tree, Angelesco Potentials, and Their Perturbations”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 5–13; Proc. Steklov Inst. Math., 311 (2020), 1–9
Citation in format AMSBIB
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\paper Discrete Schr\"odinger Operator on a Tree, Angelesco Potentials, and Their Perturbations
\inbook Analysis and mathematical physics
\bookinfo Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 311
\pages 5--13
\publ Steklov Math. Inst.
\publaddr Moscow
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  • https://doi.org/10.4213/tm4124
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    • This publication is cited in the following 7 articles:
    1. Evgeny L. Korotyaev, “The number of eigenvalues of discrete Hamiltonian periodic in time”, Journal of Mathematical Analysis and Applications, 2025, 129294  crossref
    2. A. I. Aptekarev, “Weak and Strong Asymptotics of Orthogonal Polynomials with Varying Weight”, J Math Sci, 278:2 (2024), 211  crossref  mathscinet
    3. V. G. Lysov, “Mnogourovnevye interpolyatsii dlya obobschennoi sistemy Nikishina na grafe-dereve”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 345–361  mathnet
    4. V. G. Lysov, “Multilevel interpolations for the generalized Nikishin system on a tree graph”, Trans. Moscow Math. Soc., –  mathnet  mathnet  crossref
    5. A. I. Aptekarev, V. G. Lysov, “Multilevel interpolation for Nikishin systems and boundedness of Jacobi matrices on binary trees”, Russian Math. Surveys, 76:4 (2021), 726–728  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. I. Aptekarev, “Slabye i silnye asimptotiki ortogonalnykh mnogochlenov c «peremennym» vesom”, Posvyaschaetsya 70-letiyu prezidenta RUDN V.M. Filippova, SMFN, 67, no. 3, Rossiiskii universitet druzhby narodov, M., 2021, 427–441  mathnet  crossref
    7. V. G. Lysov, “Mixed Type Hermite–Padé Approximants for a Nikishin System”, Proc. Steklov Inst. Math., 311 (2020), 199–213  mathnet  crossref  crossref  mathscinet  isi  elib
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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