引言多复变数函数论在近十多年来发展得比较迅速,究其原因,有如下两方面:首先,它的绝大部分不是单复变数情形的简单推广,所以提出的许多问题都不是单复变数时所存在的问题。这既说明了多复变数函数论和单复变数函数论有着本质上的差别,也说明了它确实能形成一个独立的学科。其次,也由于它在实际应用中必然地会有巨大的作用。大家都知道单复变数函数论在实际问题中有广泛应用,多复变数函数论和实际问题的联系,目前也露出一些苗头。例如它在量子埸论的色散关系中的应用。多复变数函数论这一学科的历史悠久,早期工作大多属于形式推广。从本世纪初,才出现一些本质的问题,因此引起了很多数学家的兴趣。然而,到现在为止,这一学科还很不成熟,还处在幼年时代。所以比起单复变数函数论的深入和丰富多采来说是相形见拙。可是,它却和许多学科有着紧密的联系。例如在研究 Introduction The function of multivariate function has developed rapidly in the past decade. The reasons are as follows: First, most of it is not a simple promotion of single complex variables, so many questions raised are not single. Problems with complex variables. This not only illustrates the essential difference between the function of multiple complex variables and the function of single complex variables, but also shows that it can indeed form an independent discipline. Second, it also has a huge effect due to its practical application. We all know that the single complex variable function theory is widely used in practical problems. The relationship between multiple complex variable function theory and practical problems has also exposed some signs. For example, its application in the dispersion relation of quantum paradox. The history of multivariate function theory has a long history. Most of the early work is in the form of promotion. Since the beginning of this century, only some essential problems have emerged, which has aroused the interest of many mathematicians. However, until now, the subject is still immature and still in its early years. Therefore, it is dwarfed by the depth and richness of the single variable function theory. However, it has close links with many disciplines. For example, in research