Spectral Invariance of SG Pseudo-Differential Operators on Lpℝn
We prove the spectral invariance of SG pseudo-differential operators on L p ℝ n , 1<p<∞, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L p ℝ n , 1<p<∞. A key ingredient in the proof is the spectral invariance of SG pseudo-differential operators on L 2ℝ n .
KeywordsPseudo-differential operators Sobolev spaces ellipticity Fredholmness spectral invariance
Mathematics Subject Classification (2000)Primary 35S05 47G30 Secondary 47A53
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