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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

Yoshinori Morimoto
Yoshinori Morimoto*
Affiliation:
Division of Mathematics, Yoshida College, Kyoto University, Kyoto 606-01, Japan, e-mail: morimoto@math.h.kyoto-u.ac.jp
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 139 , September 1995 , pp. 151 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

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