We consider a class of analytic functions that are closely related to approximate conformal mappings of simply connected domains onto the unit disk. Using a result of Warschawski, we improve upon our estimates of the argument in the considered class for the important case when the mapping is nearly
Some results on functions of matrix argument
β Scribed by A. M. Mathai
- Publisher
- John Wiley and Sons
- Year
- 1978
- Tongue
- English
- Weight
- 315 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
Abstract
A number of integrals of scalar variables are extended to the case of matrix variables. Functions where the argument is a positive definite symmetric matrix are considered in this article. With the help of a generalized matrix transform a number of results are derived which are extensions of the corresponding results in the univariate cases.
π SIMILAR VOLUMES
Let \ be a nonnegative homogeneous function on R n . General structure of the set of numerical pairs ($, \*), for which the function (1&\ \* (x)) $ + is positive definite on R n is investigated; a criterion for positive definiteness of this function is given in terms of completely monotonic function
## Abstract We construct an algorithm that allows us to determine an effective canonical factorization of some nonβrational matrixβvalued functions. For those matrixβvalued functions whose entries can be represented through a innerouter factorization (when the outer function is rational) it is show