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Proceedings of the American Mathematical Society

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On a characterisation of matrix functions which are differences of two monotone matrix functions


Author: Harkrishan Vasudeva
Journal: Proc. Amer. Math. Soc. 32 (1972), 531-534
MSC: Primary 26A48; Secondary 15A57
DOI: https://doi.org/10.1090/S0002-9939-1972-0293035-6
MathSciNet review: 0293035
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Abstract: The class of matrix functions of 'bounded variation' was introduced by O. Dobsch in a paper published in 1937 [2]. The consideration of this class of functions immediately gives rise to the consideration of those matrix functions of order n on an interval [a, b] that are representable as the difference of two monotone matrix functions on that interval. Such a difference will have high regularity properties when n is large and is therefore much more than simply a function of bounded variation. The characterization of this class was sought in the paper of Dobsch [2]. The purpose of this paper is to give a complete description of a related class: the functions defined on (--1,1) which have restrictions to any closed subinterval which are such differences.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293035-6
Article copyright: © Copyright 1972 American Mathematical Society