Formulations variationnelles de l’addition parallèle et de la soustraction parallèle d’opérateurs semi-définis positifs. (Variational formulations of the parallel addition and of the parallel subtraction of positive semi-definite operators). (French) Zbl 0597.15008

Hiriart-Urruty, Jean-Baptiste; Mazure, Marie-Laurence

C. R. Acad. Sci., Paris, Sér. I 302, 527-530 (1986).

The parallel addition and subtraction of symmetric positive semi-definite operators as a result of convolution-deconvolution operators acting on the convex functions are described. Some examples needing this mathematical analysis are mentioned. The proofs are often extended to discuss supplementary theorems which cover the image operators.

Reviewer: D.Voukalis

MSC:

15A30	Algebraic systems of matrices
94A05	Communication theory

Keywords:

parallel sum; parallel difference; convex analysis; parallel addition and subtraction; symmetric positive semi-definite operators; convolution- deconvolution operators