bergman series 中文意思是什麼
bergman series
解釋
伯格曼系-
For some non - symmetric homogeneous domains, we can also get the explicit formulas of their bergman kernel functions by hua method [ xu4 ] [ gi ]. we know the complete orthonormal system of the bounded reinhardt domain made up of monomials, and complex ellipsoid domain is the bounded reinhardt domain, so the explicit formulas of the bergman kernel functions are obtained by summing an infinite series in some cases ( called method of summing series )
對於一些非對稱的齊性域，也可以用華羅庚方法得到它們的bergman核函數的顯表達式我們知道，有界reinhardt域的完備標準正交系由單項式組成，而復橢球域是包含原點且以原點為中心的有界reinhardt域，於是可以通過無窮級數求和函數的方法，計算其bergman核函數的顯表達式，這種求bergman核函數的顯表達式的方法稱為級數法。 -
The generalized hua domains are neither homogeneous domains nor reinhardt domains. so we can not, use the hua method or the method of summing a series to get bergman kernel functions in explicit forms
由於在一般情況下廣義華羅庚域既不是有界齊性域，也不是有界reinhardt域，因此既不能用華羅庚方法，也無法用級數法得到其b 。 -
The first chapter of this article consists of the following contents. suppose that are positive integers., then the bergman kernel function for the second type of hua domain where determined by the following recursion formula : and where is determined by the following recursion formula : it is inappropriate to use holomorphic transitive group to compute the bergman kernel function of hen because he11 is not a homogeneous domain, and we can not obtain the bergman kernel function of hen by obtaining the sum of an infinite series as we compute the bergman kernel function of reinhardt domain. we firstly give some holomorphic automorphisms such that for any he there exists a holomorphic automorphism satisfying next, we introduce the concept of semi reinhardt domain and get its complete orthonormal system
結合上述兩種方法就可獲得he _的bergman核函數的顯表達式，對于兩類廣義例外華羅庚域，還要用到jordantriplesystem的理論，才能求出其bergman核函數的顯表達式： 2當是正整數，時，廣義例外華羅庚域的bergman核函數其中滿足如下的等式：於是，可從等式得到所有的a _ j ， ry u dstu thalca000ereereereforfortheerethettithen其中廣； k由下歹遞推公式決定： 。
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