Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator, and positive quadratic forms. But there are many applications like the crystallographic X-ray transform or the ultrahyperbolic Dirac operator which are closely connected with indefinite quadratic forms. Although appearing in many papers in such cases Hilbert modules are not the right choice as function spaces since they do not reflect the induced geometry. In this paper we are going to show that Clifford-Krein modules are naturally appearing in this context. Even taking into account the difficulties, e.g., the existence of different inner products for duality and topology, we are going to demonstrate how one can work with them Taking into account possible applications and the nature of hypercomplex analysis, special attention will be given to the study of Clifford-Krein modules with reproducing kernels. In the end we will discuss the interpolation problem in Clifford-Krein modules with reproducing kernel.

经典的超复杂分析与椭圆算子（例如Laplacian或Dirac算子）和正二次形密切相关。但是，存在许多应用，例如晶体学X射线变换或超双曲Dirac算子，它们与不确定的二次形式紧密相连。尽管在这种情况下出现在许多论文中，希尔伯特模块作为函数空间并不是正确的选择，因为它们不能反映出诱导的几何形状。在本文中，我们将证明在这种情况下自然会出现Clifford-Krein模块。即使考虑到各种困难（例如，存在用于双重性和拓扑结构的不同内部产品），我们仍将展示如何与它们一起使用，同时考虑到可能的应用程序和超复杂分析的性质，将特别关注具有可再生内核的Clifford-Krein模块的研究。最后，我们将讨论带有再生内核的Clifford-Krein模块中的插值问题。