The spectral density of Hankel operators with piecewise continuous symbols

Emilio Fedele

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arXiv · 1903.11572

The spectral density of Hankel operators with piecewise continuous symbols

Emilio Fedele

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Abstract

In 1966, H. Widom proved an asymptotic formula for the distribution of eigenvalues of the $N\times N$ 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).

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Emilio Fedele. 2019-03-27. The spectral density of Hankel operators with piecewise continuous symbols. https://arxiv.org/abs/1903.11572

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