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Proceedings of the American Mathematical Society

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

 
 

 

Weak spectral theory


Author: M. W. Wong
Journal: Proc. Amer. Math. Soc. 95 (1985), 429-432
MSC: Primary 35S05; Secondary 47G05
DOI: https://doi.org/10.1090/S0002-9939-1985-0806082-9
MathSciNet review: 806082
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Abstract | References | Similar Articles | Additional Information

Abstract: We initiate the weak spectrum of a linear operator on $ {L^p}$ spaces, $ 1 \leqslant p < \infty $. The weak spectrum of a pseudo-differential operator with symbol in $ S_{\alpha \sigma }^m$, where $ - \infty < m < \infty $ and $ 0 \leqslant \rho \leqslant 1$, is investigated.


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

  • [1] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36. MR 0257819 (41:2468)
  • [2] M. Schechter, Spectra of partial differential operators, North-Holland, Amsterdam, 1971. MR 869254 (88h:35085)
  • [3] M. W. Wong, Spectra of pseudo-differential operators on $ {L^p}({{\mathbf{R}}^n})$, Comm. Partial Differential Equations 4 (1979), 1389-1401. MR 551657 (81a:47052)
  • [4] -, On some exotic pseudo-differential operators, Comm. Partial Differential Equations 5 (1980), 733-739. MR 579994 (81h:47045)
  • [5] -, $ {L^p}$-spectra of strongly Carleman pseudo-differential operators, J. Funct. Anal. 44 (1981), 163-173. MR 642915 (83b:47057)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0806082-9
Keywords: Spectrum, weak spectrum, multipliers, weak type $ (p,p)$, pseudo-differential operators
Article copyright: © Copyright 1985 American Mathematical Society

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