## The diagonal of the Padé table and the approximation of the Weyl function of second order difference operators (1995)

by
Bernhard Beckermann
,
Valeri Kaliaguine

Citations: | 6 - 4 self |

### BibTeX

@MISC{Beckermann95thediagonal,

author = {Bernhard Beckermann and Valeri Kaliaguine},

title = {The diagonal of the Padé table and the approximation of the Weyl function of second order difference operators},

year = {1995}

}

### OpenURL

### Abstract

We study connections between diagonal Padé approximants and spectral properties of second order difference operators with complex coefficients. In a first part, we identify the diagonal of the Padé table with a particular difference operator which is shown to have maximal resolvent set. The spectrum of an asymptotically periodic complex difference operator is given, and we prove convergence on the resolvent set for the corresponding sequence of Padé approximants to the associated Weyl function.