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
Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally bi...Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))-1f(x) ∈ Mg and f(x) - x has a zero of order k + 1 at x = 0. We obtain coeffcient estimates for f(x). These results unify and generalize many known results.展开更多
We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimat...We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.展开更多
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.
基金supported by National Natural Science Foundation of China (Grant No. 10571164)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20050358052)+1 种基金the Jiangxi Provincial Natural Science Foundation of China (Grant No. 2007GZS0177)Specialized Research Fund for the Doctoral Program of Jiangxi Normal University
文摘Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))-1f(x) ∈ Mg and f(x) - x has a zero of order k + 1 at x = 0. We obtain coeffcient estimates for f(x). These results unify and generalize many known results.
基金National Basic Research Program of China(973 Program No.2007CB814903)the National Natural Science Foundation of China(No.70671069)
文摘We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.
