La soustraction parallèle d’operateurs Interprétée comme déconvolution de formes quadratiques convexes

Abstract

In the set of all symmetric positive semi-definite operators on the finite-dimensional space , parallel substraction appears, to a certain extent, as the inverse operation of parallel addition, Now, parallel addition may be interpreted through inf-convolution of convex quadratic forms; in the same way, the variational formulation of parallel substraction leads us to what we call the de-convolution of a convex function by another one. Properties of parallel substraction are thus deduced from those of the so-called operation of de-convolution for convex quadratic forms.

AMS 1980 Subject Classifications:

• Primary: 90 C 25
• Secondary: 49 H 05
• Secondary: 15 A 63

Keywords:

• Parallel addition and subtraction
• convex partially quadratic forms
• conjugacy operation
• informal convolution
• de-convolution