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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A pseudo differential operator which shifts the wave front set


Authors: Cesare Parenti and Luigi Rodino
Journal: Proc. Amer. Math. Soc. 72 (1978), 251-257
MSC: Primary 35S05
MathSciNet review: 507317
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Abstract: The note concerns pseudo differential operators in the classes $ L_{\rho ,1}^m,0 < \rho \leqslant 1$. These operators are pseudo-local, but they can displace the wave front set of distributions, as we show by means of an example in $ L_{1,1}^0$.


References [Enhancements On Off] (What's this?)

  • [1] Richard Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1–42. MR 0367730
  • [2] Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 0388463
  • [3] Lars Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math. (2) 17 (1971), 99–163. MR 0331124
  • [4] L. Nirenberg, Pseudo-differential operators, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 149–167. MR 0270217

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507317-9
Keywords: Pseudo differential operator, class $ S_{\rho ,\delta }^m$, class $ L_{\rho ,\delta }^m$, pseudo-local operator, wave front set
Article copyright: © Copyright 1978 American Mathematical Society