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Spectral Invariance of SG Pseudo-Differential Operators on L pℝn

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Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 205))

Abstract

We prove the spectral invariance of SG pseudo-differential operators on L pℝn, 1<p<∞, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L pℝn, 1<p<∞. A key ingredient in the proof is the spectral invariance of SG pseudo-differential operators on L 2ℝn.

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References

  1. A. Dasgupta, Ellipticity of Fredholm pseudo-differential operators on L pℝn, in New Developments in Pseudo-Differential Operators, Editors: L. Rodino and M. W. Wong, Operator Theory: Advances and Applications 189, Birkhäuser, 2008, 107–116.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Aparajita Dasgupta

  2. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

Authors
  1. Aparajita Dasgupta
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  2. M. W. Wong
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Bert-Wolfgang Schulze

  2. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Dasgupta, A., Wong, M.W. (2009). Spectral Invariance of SG Pseudo-Differential Operators on L pℝn . In: Schulze, BW., Wong, M.W. (eds) Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations. Operator Theory: Advances and Applications, vol 205. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0198-6_2

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