A Hilbert-Schmidt integral operator and the Weil distribution
Classical Analysis and ODEs
2024-04-23 v1
Abstract
In this paper, a positive operator is given. It is shown that the product of this positive operator and the convolution operator is a trace class Hilbert-Schmidt integral operator and has nonnegative eigenvalues. A formula is given for the trace of this product operator. It seems that this product operator is the closest trace class integral operator which has nonnegative eigenvalues and is related to the Weil distribution. A relation is given between the trace of the product operator and the Weil distribution.
Keywords
Cite
@article{arxiv.2404.13427,
title = {A Hilbert-Schmidt integral operator and the Weil distribution},
author = {Xian-Jin Li},
journal= {arXiv preprint arXiv:2404.13427},
year = {2024}
}