چكيده به لاتين
In this thesis we study on some spectral properties of pseudo-differential operators and also some of their applications in the theory of partial differential equations on some specific spaces.
More precisely, we present a formula for the adjoint of pseudo-differential operators on L2(Tn) and L2(Zn) with respect to their symbols, which yields us to a necessary and sufficient condition for self-adjointness of these operators. By a similar method, we also get some results about normal and unitary properties of these operators.
Then we investigate about necessary and/or sufficient conditions for invertibility of pseudo-differential operators on Lp(Tn); p>= 1. Then as consequences of our result in this section, we obtain some corollaries for spectrum of these operators. Finally we study some applications of these operators in solving partial differential equations.
Keywords: Pseudo-Differential Operators, Symbol Classes, Boundedness, Compactness, Adjoint Operator, Normal Operator, Unitary Operator, elliptic Operator, Parametrix Operator.
