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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A pseudo differential operator which shifts the wave front set
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by Cesare Parenti and Luigi Rodino PDF
Proc. Amer. Math. Soc. 72 (1978), 251-257 Request permission

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
  • Richard Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1โ€“42. MR 367730
  • Lars Hรถrmander, Fourier integral operators. I, Acta Math. 127 (1971), no.ย 1-2, 79โ€“183. MR 388463, DOI 10.1007/BF02392052
  • Lars Hรถrmander, On the existence and the regularity of solutions of linear pseudo-differential equations, Enseign. Math. (2) 17 (1971), 99โ€“163. MR 331124
  • L. Nirenberg, Pseudo-differential operators, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp.ย 149โ€“167. MR 0270217
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • 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