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 formu...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.展开更多
Every nontrivial zero of the Riemann zeta function is associated as eigenvalue with an eigenfunction of the fundamental differential operator on a Hilbert-P′olya space. It has geometric multiplicity one. A relation b...Every nontrivial zero of the Riemann zeta function is associated as eigenvalue with an eigenfunction of the fundamental differential operator on a Hilbert-P′olya space. It has geometric multiplicity one. A relation between nontrivial zeros of the zeta function and eigenvalues of the convolution operator is given. It is an analogue of the Selberg transform in Selberg’s trace formula. Elements of the Hilbert-P′olya space are characterized by the Poisson summation formula.展开更多
The eigenvalues of a differential operator on a Hilbert-Polya space are determined.It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ■-function.Moreover,their corresponding multiplici...The eigenvalues of a differential operator on a Hilbert-Polya space are determined.It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ■-function.Moreover,their corresponding multiplicities are the same.展开更多
The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function fo...The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.展开更多
文摘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.
文摘Every nontrivial zero of the Riemann zeta function is associated as eigenvalue with an eigenfunction of the fundamental differential operator on a Hilbert-P′olya space. It has geometric multiplicity one. A relation between nontrivial zeros of the zeta function and eigenvalues of the convolution operator is given. It is an analogue of the Selberg transform in Selberg’s trace formula. Elements of the Hilbert-P′olya space are characterized by the Poisson summation formula.
基金Boqing Xue’s work is supported by the National Natural Science Foundation of China(Grant No.11701549).
文摘The eigenvalues of a differential operator on a Hilbert-Polya space are determined.It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ■-function.Moreover,their corresponding multiplicities are the same.
基金supported by the National Natural Science Foundation of China (No. 11171229)supported by 973 program (Grant No. 2011CB711100)
文摘The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.
