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

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Cardoso I., Saal L.

Colloquium Mathematicum

2012

tom 129

nr 2

263-288

Let p,q,n be natural numbers such that p+q = n. Let 𝔽 be either ℂ, the complex numbers field, or ℍ, the quaternionic division algebra. We consider the Heisenberg group N(p,q,𝔽) defined 𝔽ⁿ × ℑ𝔪 𝔽, with group law given by (v,ζ)(v',ζ') = (v + v', ζ + ζ'- 1/2 ℑ𝔪 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,𝔽) be the group of n × n matrices with coefficients in 𝔽 that leave the form B invariant. We compute explicit fundamental solutions of some second order differential operators on N(p,q,𝔽) which are canonically associated to the action of U(p,q,𝔽).

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1 Colloquium Mathematicum

1 Cardoso I.

1 Saal L.

1 2012

Wyniki wyszukiwania

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