A Hilbert-Schmidt integral operator and the Weil distribution  

作　　者：Xian-Jin Li 

机构地区：[1]Department of Mathematics,Brigham Young University,Provo,UT 84602,USA

出　　处：《Science China Mathematics》2023年第1期91-114,共24页中国科学：数学（英文版）

摘　　要：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 in the context of Connes’program for the Riemann hypothesis.A relation is given between the trace of the product operator and the Weil distribution.

关 键 词：EIGENVALUE explicit formula POSITIVITY trace of the operator 

分 类 号：O177[理学—数学]