THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Let G = SU(2,2), K = S(U(2)×U(2)), and for l∈Z, let {τl}l∈z be a onedimensional K-type and let El be the line bundle over G/K associated to τl. It is shown that the τl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.     

HEAT KERNELS AND HARDY＇S UNCERTAINTY PRINCIPLE ON H-TYPE GROUPS

This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.     

H型群上的非线性Liouville定理

对H型群上的次线性方程△Gu+up=0进行了研究,其中△G是对应的sublaplace算子.通过将移动平面方法推广到H型群上,证明了在一定条件下的p和函数u,次线性方程△Gu+up=0的唯一解是u≡0.     

Modified Gram-Schmidt-based methods for block downdating the Cholesky factorization

The hyperbolic modified Gram-Schmidt (HMGS) method is proposed for block downdating the Cholesky factorization. The method might be unsatisfactory due to rounding errors. A modified version based on the MGS process is presented and is shown to be mixed stable. Numerical tests show that the new method has the same numerical properties as the generalized LINPACK-type algorithm, and can work better than the Householder-based algorithm given by Bojanczyk and Steinhardt (1991) [9].