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On some spectral properties of elliptic pseudodifferential operators

Author: M. W. Wong
Journal: Proc. Amer. Math. Soc. 99 (1987), 683-689
MSC: Primary 47G05; Secondary 35S05
MathSciNet review: 877040
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Abstract: We prove that the minimal and maximal operators associated with an elliptic pseudodifferential operator coincide in $ {L^p}({{\mathbf{R}}^n}),1 < p < \infty $. We obtain a set of necessary and sufficient conditions for a measurable function $ q$ on $ {{\mathbf{R}}^n}$ to be compact relative to some integral power of a constant coefficient elliptic pseudodifferential operator.

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

  • [1] E. Balslev, The essential spectrum of elliptic operators in $ {L^p}({{\mathbf{R}}^n})$, Trans. Amer. Math. Soc. 116 (1965), 193-217. MR 0190524 (32:7936)
  • [2] K. Gustafson and J. Weidmann, On the essential spectrum, J. Math. Anal. Appl. 25 (1969), 121-127. MR 0242004 (39:3339)
  • [3] H. Kumano-go, Psuedo-differential operators, MIT Press, 1981.
  • [4] M. Schechter, On the essential spectrum of an arbitrary operator. I, J. Math. Anal. Appl. 13 (1966), 205-215. MR 0188798 (32:6230)
  • [5] -, Spectra of partial differential operators, North-Holland, Amsterdam, 1971.
  • [6] -, Principles of functional analysis, Academic Press, New York, 1971. MR 0445263 (56:3607)
  • [7] M. W. Wong, $ {L^p}$-spectra of strongly Carleman pseudo-differential operators, J. Funct. Anal. 44 (1981), 163-173. MR 642915 (83b:47057)
  • [8 M] W. Wong, Fredholm pseudo-differential operators on weighted Sobolev spaces, Ark. Mat. 21 (1983), 271-282. MR 727349 (85d:47054)

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Keywords: Elliptic pseudodifferential operators, minimal operators, maximal operators, relative compactness
Article copyright: © Copyright 1987 American Mathematical Society

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