Abstract
The concept of pseudodifferential oper ators (PDO) is introduced as a generalization of the usual concepts of differential and integral operators. Based on the PDO concept in Euc1idean spaces the concept of a PDO on a manifold is developed. It is demonstrated that for PDOs on a manifold the main part of the operator coincides with the usual planar approximation of the operator. The so-called Meissl scheme is identified as the direct consequence of the homomorphy of the algebra of PDOs and the algebra of their symbols.
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