# The spectral density of Hankel operators with piecewise continuous symbols

## TL;DR

This paper extends Widom's asymptotic eigenvalue distribution formula to Hankel matrices with piecewise continuous symbols, showing the distribution's independence from truncation method.

## Contribution

It generalizes Widom's formula to a broader class of Hankel matrices and proves truncation independence of eigenvalue distribution.

## Key findings

- Eigenvalue distribution formula extended to piecewise continuous symbols
- Distribution is independent of truncation method
- Results generalize classical Hilbert matrix analysis

## 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).