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

• Autorzy: Isolda Cardoso , Linda Saal
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 43A80: Analysis on other specific Lie groups
• 35A08: Fundamental solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 2
• Strony: 263-288

Daty

wydano

2012

Twórcy

autor

Isolda Cardoso

• ECEN-FCEIA, Universidad Nacional de Rosario, Pellegrini 250, 2000 Rosario, Argentina

autor

Linda Saal

• FAMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina

Identyfikatory

DOI

10.4064/cm129-2-7