Bernhard Beckermann
On the classification of the spectrum of second order
difference operators
Key words : Second order difference operator, spectrum,
Weyl function, formal orthogonal polynomials, Jacobi matrix, $J$--fraction.
Classifications: AMS(MOS): 47A10, 39A70, 47B39, 40A15.
Abstract
We study nonsymmetric second order difference operators acting in the
Hilbert space $ell^2$ and describe the resolvent set and the essential
spectrum of such operators in terms of related formal orthogonal
polynomials.