Spectral theory of Jacobi matrices on trees whose coefficients are generated by multiple orthogonality. (English) Zbl 07466427
Authors’ abstract: We study 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 large classes of orthogonality measures.
Reviewer: Bilender P. Allahverdiev (Isparta)
MSC:
| 47B36 | Jacobi (tridiagonal) operators (matrices) and generalizations |
| 47A10 | Spectrum, resolvent |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
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