The Spectral Density of Hankel Operators with Piecewise Continuous Symbols

Emilio Fedele

doi:10.1007/s00020-019-2556-9

The Spectral Density of Hankel Operators with Piecewise Continuous Symbols

Emilio Fedele

Mathematics

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Abstract

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).

Original language	English
Article number	1
Journal	INTEGRAL EQUATIONS AND OPERATOR THEORY
Volume	92
Issue number	1
Early online date	30 Nov 2019
DOIs	https://doi.org/10.1007/s00020-019-2556-9
Publication status	Published - 1 Feb 2020

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The Spectral Density of Hankel Operators with Piecewise Continuous Symbols

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