A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis. The result is then applied to determine the distance between a point and a G-orbit or its convex hull.We also discuss the derivatives of some orbital functions.
@article{bwmeta1.element.doi-10_1515_spma-2016-0033,
author = {Tin-Yau Tam and William C. Hill},
title = {Derivatives of orbital function and an extension of Berezin-Gel'fand's theorem},
journal = {Special Matrices},
volume = {4},
year = {2016},
zbl = {06672753},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0033}
}
Tin-Yau Tam; William C. Hill. Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem. Special Matrices, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0033/