The Heisenberg ultrahyperbolic equation: \(K\)-finite and polynomial solutions

DOI10.1215/21562261-1728911zbMath1287.22003OpenAlexW2072078754MaRDI QIDQ1928328

Anthony C. Kable

Publication date: 3 January 2013

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.kjm/1352987538

zbMATH Keywords

PDEconformal invarianceHeisenberg ultrahyperbolic operatorutrahyperbolic equation

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Polynomial solutions to PDEs (35C11)

Related Items (4)

Special values for conformally invariant systems associated to maximal parabolics of quasi-Heisenberg type ⋮ Fundamental solutions of a class of ultra-hyperbolic operators on pseudo \(H\)-type groups ⋮ The structure of the space of polynomial solutions to the canonical central systems of differential equations on the block Heisenberg groups: a generalization of a theorem of Korányi ⋮ On the space of 𝐾-finite solutions to intertwining differential operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Heisenberg ultrahyperbolic equation: the basic solutions as distributions
• \(K\)-finite solutions to conformally invariant systems of differential equations
• Conformally invariant systems of differential operators
• Kelvin transforms and harmonic polynomials on the Heisenberg group
• Degenerate principal series representations of \(GL_n(\mathbb{C})\) and \(GL_n(\mathbb{R})\)
• Analysis on the minimal representation of \(O(p,q)\). I: Realization via conformal geometry.
• Analysis on the minimal representation of \(\mathrm O(p,q)\). II: Branching laws.
• Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\)
• Representations of \(\text{SU}(p,q)\) and CR geometry. I
• The ultrahyperbolic differential equation with four independent variables
• The structures of standard (g,K)-modules of SL(3,R)
• Lie groups beyond an introduction

This page was built for publication: The Heisenberg ultrahyperbolic equation: \(K\)-finite and polynomial solutions