第I类非自共轭锥上的Gamma函数

The Gamma Functions on Nonselfdual Cones of the First Type

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ｉ类非自共轭锥上．作为其应用，显式给出了以这些锥为底的管状域（或第一类Ｓｉｅｇｅｌ域）的ＣａｕｃｈｙＳｚｅｇ¨ｏ核和形式Ｐｏｉｓｏｎ核．

In this paper, we generalize the Gamma function and Siegel integral to nonselfdual cones of the first type. As the applications, the Cauchy Szeg kernels and formal Poisson kernels on the tube domains(or Siegel domains of the first type)over such nonselfdual cones are given in the explicit forms.