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Local solvability and hypoellipticity for pseudodifferential operators of Egorov type with infinite degeneracy
Published online by Cambridge University Press: 22 January 2016
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Let P be a pseudodifferential operator of the form
where s, b ≥ 0 are even integers and is odd function with f′(t) > 0 (t ≠ 0). Here . We shall call P an operator of Egorov type because P with f(t) = tk, (k odd) is an important model of subelliptic operators studied by Egorov [1] and Hörmander [3], [4, Chapter 27]. Roughly speaking, any subelliptic operator can be reduced to this operator or Mizohata one after several steps of microlocalization arguments. In this paper we shall study the hypoellipticity of P and the local solvability of adjoint operator P* in the case where f(t) vanishes infinitely at the origin and moreover consider the case where ts and are replaced by functions with zero of infinite order.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1995
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