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On the spectrum of tridiagonal operators in the context of orthogonal polynomials.
Acta Sci. Math., DOI: 10.1007/s44146-023-00106-6 (2024)
The basis for our studies is a large class of orthogonal polynomial sequences (Pn)n∈N0, which is normalized by Pn(x0)=1 for all n∈N0 where the coefficients in the three-term recurrence relation are bounded. The goal is to check if x0∈R is in the support of the orthogonalization measure μ. For this purpose, we use, among other things, a result of G. H. Hardy concerning Cesàro operators on weighted l2-spaces. These investigations generalize ideas from Lasser et al. (Arch Math 100:289–299, 2013).
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
33d45 ; 47b36 ; Cesàro Operators ; Growth Of Derivatives ; Orthogonal Polynomials ; Spectrum ; Tridiagonal Operators
ISSN (print) / ISBN
0001-6969
Journal
Acta Scientiarum Mathematicarum
Publisher
Bolyai Institute, University of Szeged
Publishing Place
233 Spring Street, 6th Floor, New York, Ny 10013 Usa
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Strategy and Digitalization (DIG)
Grants
Helmholtz Zentrum Mnchen - Deutsches Forschungszentrum fr Gesundheit und Umwelt (GmbH) (4209)