In this paper the authors give a definite meaning to any formal trigonometrical series and generalize it to all abstract Hilbert space. Then in the case L-2(-infinity + infinity) they discussed extensively the general...In this paper the authors give a definite meaning to any formal trigonometrical series and generalize it to all abstract Hilbert space. Then in the case L-2(-infinity + infinity) they discussed extensively the generalized expansion problem by Hermite functions, and applied to a non-strictly nonlinear hyperbolic system.展开更多
1. Introduction It is very important to study the theory of the multidimensional hyperbolic conservation laws. A typical model is the following initial value problem
A compactness frame of the Lax-Friedrichs scheme for the equations of gas dynamics is obtained by using some embedding theorems and an analysis of the difference scheme and the weak entropy.
This paper contillues the study of [1] on weak functions. The weak convergence theory is investigated in complex analysis, Fourier transform and Mellin transform. A Mobius inverse formula of weak functions is obtained.
In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they sol...In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they solve the problem of the multiplication of two generalized functions.展开更多
This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
In this paper, the authors introduce some Mellin transforms in weak functions and discuss their applications to Miints formula of the Riemann zeta-function.
This paper treats Dirichlet series from the point of view developed in [1],[2]. Especially it is found that the kernal function is closely related with the Riemann Zeta-function.
This paper discusses two problems. Firstly the authors give the Schwarz formula for a holomorphic function in unit disc when the boundary value of its real part is in the class H of generalized functions in the sense ...This paper discusses two problems. Firstly the authors give the Schwarz formula for a holomorphic function in unit disc when the boundary value of its real part is in the class H of generalized functions in the sense of Hua. Secondly the authors use the classical Schwarz formula to give a new proof of the zero free region of the Riemann zeta-function.展开更多
文摘In this paper the authors give a definite meaning to any formal trigonometrical series and generalize it to all abstract Hilbert space. Then in the case L-2(-infinity + infinity) they discussed extensively the generalized expansion problem by Hermite functions, and applied to a non-strictly nonlinear hyperbolic system.
文摘1. Introduction It is very important to study the theory of the multidimensional hyperbolic conservation laws. A typical model is the following initial value problem
文摘A compactness frame of the Lax-Friedrichs scheme for the equations of gas dynamics is obtained by using some embedding theorems and an analysis of the difference scheme and the weak entropy.
文摘This paper contillues the study of [1] on weak functions. The weak convergence theory is investigated in complex analysis, Fourier transform and Mellin transform. A Mobius inverse formula of weak functions is obtained.
文摘In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they solve the problem of the multiplication of two generalized functions.
文摘This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
文摘In this paper, the authors introduce some Mellin transforms in weak functions and discuss their applications to Miints formula of the Riemann zeta-function.
文摘This paper treats Dirichlet series from the point of view developed in [1],[2]. Especially it is found that the kernal function is closely related with the Riemann Zeta-function.
文摘This paper discusses two problems. Firstly the authors give the Schwarz formula for a holomorphic function in unit disc when the boundary value of its real part is in the class H of generalized functions in the sense of Hua. Secondly the authors use the classical Schwarz formula to give a new proof of the zero free region of the Riemann zeta-function.
