The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. Th...The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.展开更多
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The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.
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.
