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
Recently, Bourgat et al.[3] gave a domain decomposition algorithm which can be implemented in parallel, and many numerical experiments have illustrated its efficiency. In this paper,we make a detailed theoretical anal...Recently, Bourgat et al.[3] gave a domain decomposition algorithm which can be implemented in parallel, and many numerical experiments have illustrated its efficiency. In this paper,we make a detailed theoretical analysis about this algorithm.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Recently, Bourgat et al.[3] gave a domain decomposition algorithm which can be implemented in parallel, and many numerical experiments have illustrated its efficiency. In this paper,we make a detailed theoretical analysis about this algorithm.
