On a characterisation of matrix functions which are differences of two monotone matrix functions
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- by Harkrishan Vasudeva PDF
- Proc. Amer. Math. Soc. 32 (1972), 531-534 Request permission
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.References
- Julius Bendat and Seymour Sherman, Monotone and convex operator functions, Trans. Amer. Math. Soc. 79 (1955), 58–71. MR 82655, DOI 10.1090/S0002-9947-1955-0082655-4
- Otto Dobsch, Matrixfunktionen beschränkter Schwankung, Math. Z. 43 (1938), no. 1, 353–388 (German). MR 1545729, DOI 10.1007/BF01181100
- Karl Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), no. 1, 177–216 (German). MR 1545446, DOI 10.1007/BF01170633
Additional Information
- © Copyright 1972 American Mathematical Society
- 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