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Seminar on Complex Analysis (Gonchar Seminar)
June 17, 2019 17:00–19:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)
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On Spectrum of a Selfadjoint Difference Operator on the Graph-Tree
A. I. Aptekarev Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
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Abstract:
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).
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