Franz Luef, Gerald Teschl
On the Finiteness of the Number of Eigenvalues of Jacobi Operators below the Essential Spectrum
The paper is published: J. Difference Equ. Appl. 10, no. 3 (2004) 299-307

MSC:

39A10 Difference equations, See also {33Dxx}

39A70 Difference operators, See also {47B39}

34B24 Sturm-Liouville theory, See also {34Lxx}

34L05 General spectral theory

Abstract: We present a new oscillation criterion to determine whether
the number of eigenvalues below the essential spectrum of
a given Jacobi operator is finite or not. As an application we show
that Kenser's criterion for Jacobi operators follows as a special case.
Keywords: Discrete oscillation theory, Jacobi operators, spectral theory, Kneser's theorem
Notes: second version with modified title