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A Hilbert-Schmidt integral operator and the Weil distribution
Published 20 Apr 2024 in math.CA | (2404.13427v1)
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.
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- J. T. Tate, Fourier analysis in number fields and Hecke’s zeta-functions, in “Algebraic Number Theory,” Edited by J.W.S. Cassels and A. Fröhlich, Academic Press, New York, 1967, 305–347.
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