Abstract
We initiate the study of the spectrum, point spectrum, continuous spectrum and residual spectrum of a constant coefficient pseudo-differential operator on the Schwartz space. The results are in sharp contrast with the corresponding ones for the Banach space Lp(Rn), 1 ≤ p ≤ ∞. An application to the study of spectra of constant coefficient pseudo-differential operators on the space of Schwartz distributions is given.
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