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On a Geometric Formula for the Fundamental Solution of Subelliptic Laplacians
Author(s) -
Beals Richard,
Gaveau Bernard,
Greiner Peter
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211810105
Subject(s) - mathematics , hypersurface , pure mathematics , mathematical analysis , variety (cybernetics) , class (philosophy) , order (exchange) , function (biology) , hamiltonian (control theory) , action (physics) , mathematical optimization , computer science , statistics , physics , finance , quantum mechanics , artificial intelligence , evolutionary biology , economics , biology
This paper introduces a new method for constructing fundamental solutions and parametrices for a class of second order subelliptic operators. The method is applied to obtain an explicit fundamental solution for the sublaplacian associated to the hypersurface [lm z 2 = |z 1 | 2 k ] ⊂ ℂ 2 . The fundamental solution is expressed as an integral over the characteristic variety of an expression whose denominator is a Hamiltonian action function and whose numerator solves an associated second order transport equation.