Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1978-0507317-9
MathSciNet review: 507317
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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] R. Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1-42. MR 51 #3972. MR 0367730 (51:3972)
  • [2] L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), 79-183. MR 52 #9299. MR 0388463 (52:9299)
  • [3] -, On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math. 17 (1971), 99-163. MR 48 #9458. MR 0331124 (48:9458)
  • [4] L. Nirenberg, Pseudo-differential operators, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R. I., 1970, pp. 149-167. MR 42 #5108. MR 0270217 (42:5108)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35S05

Retrieve articles in all journals with MSC: 35S05


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

American Mathematical Society