An elementary symmetry-based derivation of the heat kernel on Heisenberg group

zbMath1337.35162MaRDI QIDQ380760

Mohammad Hasan, H. S. Yoon

Publication date: 14 November 2013

Published in: African Diaspora Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.adjm/1375293538

zbMATH Keywords

Heisenberg groupfundamental solutionheat kernelseparation of variablesLie symmetry

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Geometric theory, characteristics, transformations in context of PDEs (35A30) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Heat kernel (35K08) Bergman spaces and Fock spaces (30H20)

Cites Work

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• Lie group symmetries as integral transforms of fundamental solutions
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Hamilton-Jacobi theory and the heat kernel on Heisenberg groups
• Separation of variables of a generalized porous medium equation with nonlinear source.
• The Green function of model step two hypoelliptic operators and the analysis of certain tangential Cauchy Riemann complexes
• Calculus on Heisenberg Manifolds. (AM-119)
• The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
• Symmetries and differential equations

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