Geronimus spectral transforms and measures on the complex plane

Authors:
F. Marcellán;J. Hernández
Affiliations:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
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Abstract

We analyze a special spectral transform of a measure @m supported on a compact subset C of the complex plane. A perturbation @m"1 of @m is said to be a Geronimus spectral transform if d@m"1=d@m|z-@a|^2 where @a@?C. We focus our attention in the analysis of the Hessenberg matrix associated with the multiplication operator in terms of the orthogonal polynomial basis defined by the measure @m"1.