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This article is cited in 8 scientific papers (total in 9 papers)
Nondegenerate subelliptic pseudodifferential operators
Yu. V. Egorov
Abstract:
In this paper we study scalar pseudodifferential operators for which the gradient $\operatorname{grad}_{x,\xi}p^0(x,\xi)$ of the principal part of the symbol does not vanish and is not proportional to a real vector at any characteristic point $(x,\xi)\in\Omega\times\{\mathbf R^n\setminus0\}$. Such operators are called nondegenerate. It is assumed in addition that for each point of $\Omega\times\{\mathbf R^n\setminus0\}$ there exists an operator in the Lie algebra generated by the operators $P$ and $P^*$ the principal part of the symbol of which does not vanish at this point. For these operators we present here hypoellipticity conditions, conditions for the local solvability of the equation $Pu=f$, a theorem on the smoothness of the solutions of this equation, and so on. All of the conditions obtained have a simple algebraic character and are exact, necessary and sufficient.
Bibliography: 13 titles.
Received: 11.06.1969
Citation:
Yu. V. Egorov, “Nondegenerate subelliptic pseudodifferential operators”, Math. USSR-Sb., 11:3 (1970), 291–309
Linking options:
https://www.mathnet.ru/eng/sm3453https://doi.org/10.1070/SM1970v011n03ABEH002071 https://www.mathnet.ru/eng/sm/v124/i3/p323
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