Remarks on Analytic Hypoellipticity and Local Solvability in the Space of Hyperfunctions

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概要

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• Let p(x,D) be a pseudodifferential operator on Rn with a ( formal) analytic symbol p(x, ξ), and let x0 ∈ Rn. In this paper we prove that the transposed operator tp(x,D) of p(x,D) is locally solvable at x0 modulo analytic functions in the space of hyperfunctions if p(x,D) is analytic hypoelliptic at x0. We also microlocalize this result.

• 東京大学の論文

著者

• Wakabayashi Seiichiro

  Institute Of Mathematics The University Of Tsukuba

関連論文

• On Hypoellipticity of the Operator ${\rm exp} [- {\mid} x_1 {\mid} ^{- \sigma}] D^2 _1+x^4 _1 D^2_2 +1$ : Dedicated to Professor Matsuhide Matsumura on his seventieth birthday
• The C^∞-well posed Cauchy problem for hyperbolic operators dominated by time functions
• Microlocal a priori estimates and the Cauchy problem I
• Microhyperbolic Operators in Gevrey Classes
• Microlocal a priori estimates and the Cauchy problem II
• Propagation of Singularities of Fundamental Solutions of Hyperbolic Mixed Problems
• Remarks on Analytic Hypoellipticity and Local Solvability in the Space of Hyperfunctions
• The hyperbolic mixed problem in Gevrey classes

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