Generalized inverse functions in the problem of regularization of two-dimensional unitary matrix functions

Volodymyr V. Pavlenkov

doi:10.20535/mmtu-2019.2-039

Authors

Volodymyr V. Pavlenkov Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine https://orcid.org/0000-0003-2314-726X

DOI:

https://doi.org/10.20535/mmtu-2019.2-039

Keywords:

Regular variation, Matrix function, Unitary matrix, Generalized inverse function

Abstract

The article deals with the regular variation at infinity of two-dimensional matrix functions. Functions of real argument which are take values in space of unitary matrixes are considered. Such functions are not always regularly varying but one can apply the change of variables $x=\varphi(t)$ to receive the regularly varying matrix function. We will use the term regularization for this procedure of variables changing. The main results of this work generalized the similar results from (Pavlenkov, 2016), where the technics of inverse functions were used. Here we will used the generalized inverse functions to obtained the main results. One of the goal of this article is to show how the theory of generalized inverse functions can be used. Also some differences between the theory of regular varying functions and the theory of regularly varying matrix functions will be shown.

References

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