The Spectral Density of Hankel Operators with Piecewise Continuous Symbols

The Spectral Density of Hankel Operators with Piecewise Continuous Symbols

In 1966, H. Widom proved an asymptotic formula for the distribution of eigenvalues of the N × N truncated Hilbert matrix for large values of N . In this paper, we extend this formula to Hankel matrices with symbols in the class of piece-wise continuous functions on the unit circle. Furthermore, we s...

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Veröffentlicht in:Integral equations and operator theory 2020-02, Vol.92 (1), Article 1
1. Verfasser: Fedele, Emilio
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Continuity (mathematics)
Eigenvalues
Hankel matrices
Mathematics
Mathematics and Statistics
Operators (mathematics)
Symbols
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Zusammenfassung:In 1966, H. Widom proved an asymptotic formula for the distribution of eigenvalues of the N × N truncated Hilbert matrix for large values of N . In this paper, we extend this formula to Hankel matrices with symbols in the class of piece-wise continuous functions on the unit circle. Furthermore, we show that the distribution of the eigenvalues is independent of the choice of truncation (e.g. square or triangular truncation).
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-019-2556-9