【摘要】 本文在文献[2]的基础上引进广义数系统,定义了以广义数为基础的广义函数(本质不同于L.Schwartz的分布),研究了勒贝格积分的推广,将这理论应用于分布,便得到对σ函数等的自然理解,对广义数应用于量子场论中,也作了一些尝试性的工作。更多还原

【Abstract】 This is a further study of the work published in [2]. A generalized number system is established. The generalized functions denote the functions with generalized number system as their domain and range space which are different essentially from the Schwartz distributions. For such functions we have defined (GNL) and (G) integrals which can be considered as the generalization of the Lebesgue integral for real functions. Dirac δ function can be naturally represented by our generalized functions. This representation is more straightforward than the Schwartz distribution, theory. Moreover, each distribution can be described by a generalized function in a natural way.In another paper entitled "Generalized number system and its applications (Ⅱ) ", (Acta Natur. Sci., Nw. Univ., 1979, No.1). We consider the applications of GNS (Generalized number system) to the quantum field theory. Using GNS, we can supply a tentative mathematical model to the renormalization theory, where the commute relation should be replaced by更多还原