Spectral Theory of Pseudo-Differential Operators on S 1
Mohammad Pirhayati · 2011
For a bounded pseudo-differential operator with the dense domain C ∞ (S 1 )o nL p (S 1 ), the minimal and maximal operator are introduced. An analogue of Agmon-Douglis-Nirenberg (1) is proved and then is used to prove the uniqueness of the closed extension of an elliptic pseudo-differential oper- ator of symbol of positive order. We show the Fredholmness of the minimal operator. The essential spectra of pseudo-differential operators on S 1 are de-