A linear combination, with negative weights, of two continuous covariance functions has been analyzed by a few authors just for special cases and only in the real domain. However, a covariance is a complex valued function: for this reason, the general problem concerning the difference of two covariance functions in the complex domain needs to be analyzed, while it does not yet seem to have been addressed in the literature; hence, exploring the conditions such that the difference of two covariance functions is again a covariance function can be considered a further property. Therefore, this paper yields a contribution to the theory of correlation, hence the results cannot be restricted to the particular field of application. Starting from the difference of two complex covariance functions defined in one dimensional Euclidean space, wide families of models for the difference of two complex covariance functions can be built in any dimensional space, utilizing some well known properties. In particular, the difference of two real covariance functions has been considered; moreover, the difference between some special isotropic covariance functions has also been analyzed. A detailed analysis of the parameters of the models involved has been proposed; this kind of analysis opens a gate for modeling, in any dimensional space, the correlation structure of a peculiar class of complex valued random fields, as well as the subset of real valued random fields. Some relevant hints about how to construct the subset of real covariance functions characterized by negative values have also been given.

一些作者已经分析了两个连续协方差函数的线性组合（负权重），仅针对特殊情况且仅在实域中进行了分析。但是，协方差是一个复值函数：因此，需要分析有关复数域中两个协方差函数之差的一般问题，而文献中似乎尚未解决。因此，探索条件以使两个协方差函数的差再次成为协方差函数可被视为另一特性。因此，本文对相关理论做出了贡献，因此结果不能局限于特定的应用领域。从在一维欧几里得空间中定义的两个复协方差函数的差开始，利用某些众所周知的属性，可以在任何维度空间中建立两个复协方差函数之差的各种模型。特别是，已经考虑了两个实际协方差函数的差；此外，还分析了一些特殊的各向同性协方差函数之间的差异。已经提出了对所涉及模型的参数的详细分析。这种分析为在任何维空间中建模复杂值随机域的特殊类的相关结构以及实值随机域的子集打开了大门。还给出了有关如何构造以负值为特征的实协方差函数子集的一些相关提示。