Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem

Tin-Yau Tam, and William C. Hill. "Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem." Special Matrices 4.1 (2016): 333-349. <http://eudml.org/doc/287138>.

@article{Tin2016,
abstract = {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.},
author = {Tin-Yau Tam, William C. Hill},
journal = {Special Matrices},
keywords = {Berezin-Gel’fand’s theorem; subdifferential; Clarke generalized gradient; Lebourg mean value theorem; Eaton triple; reduced triple; finite reflection group; Berezin-Gel'fand's theorem; Lebourg mean value theorem},
language = {eng},
number = {1},
pages = {333-349},
title = {Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem},
url = {http://eudml.org/doc/287138},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Tin-Yau Tam
AU - William C. Hill
TI - Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 333
EP - 349
AB - 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.
LA - eng
KW - Berezin-Gel’fand’s theorem; subdifferential; Clarke generalized gradient; Lebourg mean value theorem; Eaton triple; reduced triple; finite reflection group; Berezin-Gel'fand's theorem; Lebourg mean value theorem
UR - http://eudml.org/doc/287138
ER -