Session S30 - Mathematical Methods in Quantum Mechanics

Friday, July 16, 20:00 ~ 20:25 UTC-3

Spectral theory of Jacobi matrices on trees whose coefficients are generated by multiple orthogonality

Sergey Denisov

University of Wisconsin - Madison, USA   -   denissov@wisc.edu

We discuss Jacobi matrices on trees whose coefficients are generated by multiple orthogonal polynomials. Hilbert space decomposition into an orthogonal sum of cyclic subspaces is obtained. For each subspace, we find generators and the generalized eigenfunctions written in terms of the orthogonal polynomials. The spectrum and its spectral type are studied for general classes of orthogonality measures.

Joint work with Alexander Aptekarev (Keldysh Institute, Russia) and Maxim Yattselev (IUPUI, USA).

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