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About essential spectra of unbounded Jacobi matrices. (English) Zbl 1497.47052

Summary: We study spectral properties of unbounded Jacobi matrices with periodically modulated or blended entries. Our approach is based on uniform asymptotic analysis of generalized eigenvectors. We determine when the studied operators are self-adjoint. We identify regions where the point spectrum has no accumulation points. This allows us to completely describe the essential spectrum of these operators.

MSC:

47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
39A22 Growth, boundedness, comparison of solutions to difference equations
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