Let p,q,n be natural numbers such that p+q = n. Let be either ℂ, the complex numbers field, or ℍ, the quaternionic division algebra. We consider the Heisenberg group N(p,q,) defined ⁿ × ℑ , with group law given by (v,ζ)(v’,ζ’) = (v + v’, ζ + ζ’- 1/2 ℑ B(v,v’)), where . Let U(p,q,) be the group of n × n matrices with coefficients in that leave the form B invariant. We compute explicit fundamental solutions of some second order differential operators on N(p,q,) which are canonically associated to the action of U(p,q,).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-2-7,
author = {Isolda Cardoso and Linda Saal},
title = {Explicit fundamental solutions of some second order differential operators on Heisenberg groups},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {263-288},
zbl = {1273.43010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-2-7}
}
Isolda Cardoso; Linda Saal. Explicit fundamental solutions of some second order differential operators on Heisenberg groups. Colloquium Mathematicae, Tome 126 (2012) pp. 263-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-2-7/