Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 5 scientific papers (total in 5 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 (5)
References:
PDF
HTML
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
\Bibitem{AptDenYat20}
\by A.~I.~Aptekarev, S.~A.~Denisov, M.~L.~Yattselev
\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
\mathnet{http://mi.mathnet.ru/tm4124}
\crossref{https://doi.org/10.4213/tm4124}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4223979}
\elib{https://elibrary.ru/item.asp?id=44961350}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2020
\vol 311
\pages 1--9
\crossref{https://doi.org/10.1134/S0081543820060012}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000614212700001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85100328655}
Linking options:
  • https://www.mathnet.ru/eng/tm4124
  • https://doi.org/10.4213/tm4124
  • https://www.mathnet.ru/eng/tm/v311/p5
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025