Explicit fundamental solutions of some second order differential operators on Heisenberg groups

Isolda Cardoso, and Linda Saal. "Explicit fundamental solutions of some second order differential operators on Heisenberg groups." Colloquium Mathematicae 129.2 (2012): 263-288. <http://eudml.org/doc/283910>.

@article{IsoldaCardoso2012,
abstract = {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 $B(v,w) = ∑_\{j=1\}^\{p\} v_\{j\}\overline\{w_\{j\}\} - ∑_\{j=p+1\}^\{n\} v_\{j\}\overline\{w_\{j\}\}$. 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,).},
author = {Isolda Cardoso, Linda Saal},
journal = {Colloquium Mathematicae},
keywords = {Heisenberg group; spherical distributions; fundamental solution},
language = {eng},
number = {2},
pages = {263-288},
title = {Explicit fundamental solutions of some second order differential operators on Heisenberg groups},
url = {http://eudml.org/doc/283910},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Isolda Cardoso
AU - Linda Saal
TI - Explicit fundamental solutions of some second order differential operators on Heisenberg groups
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 2
SP - 263
EP - 288
AB - 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 $B(v,w) = ∑_{j=1}^{p} v_{j}\overline{w_{j}} - ∑_{j=p+1}^{n} v_{j}\overline{w_{j}}$. 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,).
LA - eng
KW - Heisenberg group; spherical distributions; fundamental solution
UR - http://eudml.org/doc/283910
ER -