Local Solvability Of First Order Differential Operators Near A Critical Point, Operators With Quadratic Symbols And The Heisenberg Group
作者: Muller Detlef
作者单位: 1SUNY at Albany, USA
刊名: Communications in Partial Differential Equations, 2019, Vol.17 (1-2), pp.305-337
来源数据库: Taylor & Francis Journal
DOI: 10.1080/03605309208820843
原始语种摘要: We study questions of solvability for operators of the form p(x,D)+b, where p(x,ξ) is a real quadratic form and bεC. 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 Schrodinger representation.
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