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Local Solvability Of First Order Differential Operators Near A Critical Point,Operators With Quadratic Symbols And The Heisenberg Group
Authors:Müller Detlef
Institution:SUNY at Albany , USA
Abstract:We study questions of solvability for operators of the form p(x,D)+b, where p(x,ξ) is a real quadratic form and b?C. As one consequence, we obtain a necessary and sufficient condition for the local solvability of operators of the form L= near the critical point x=0, and prove the existence of tempered fundamental solutions whenever L is locally solvable.Our analysis of these operators is largely based on recent results about the solvabilitiy of left–invariant second order differential operators on the Heisenberg group and a transference principle for the Schrödinger representation.
Keywords:
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