Fundamental solutions for partial differential equations with reflection group invariance

DOI10.1063/1.530964zbMath0872.35003OpenAlexW2062727757MaRDI QIDQ4873282

Yuri Molchanov, Yuri Yu. Berest

Publication date: 15 October 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530964

zbMATH Keywords

Huygens' principleCoxeter groupintertwining operatorsWeyl-Heisenberg algebraDunkl differential-difference operatorCalogero-type potentialsubalgebra of mastersymmetries

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (11)

Non-Laplacian growth, algebraic domains, and finite reflection groups ⋮ A survey on Huygens' principle ⋮ Stepwise gauge equivalence of differential operators ⋮ An application of the Fourier method of separation of variables to constructing exactly solvable deformations of partial differential operators ⋮ New applications of quantum algebraically integrable systems in fluid dynamics ⋮ Non-Laplacian growth: exact results ⋮ Solution of the Hadamard problem in the class of stepwise gauge-equivalent deformations of homogeneous differential operators with constant coefficients ⋮ Markov processes related with Dunkl operators ⋮ The problem of lacunas and analysis on root systems ⋮ Gauge-equivalent deformations of linear ordinary differential operators with constant coefficients ⋮ On integrability and exact solvability in deterministic and stochastic Laplacian growth

Cites Work

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• Some applications of hypergeometric shift operators
• The Dunkl transform
• Algebraic integrability for the Schrödinger equation and finite reflection groups
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• Commutative rings of partial differential operators and Lie algebras
• Hadamard's problem and Coxeter groups: New examples of Huygens' equations
• An elementary approach to the hypergeometric shift operators of Opdam
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
• A property of the family of quadratic maps with stochastic dynamics under a parametric action
• Exchange operator formalism for integrable systems of particles

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