Standard Pseudodifferential Operators
This chapter is the basic one in the book and, I hope, the most elementary. Its contents are essentially the definitions and fundamental properties of what are called here standard pseudodifferential operators, often called operators of type (1, 0), to contrast them with operators of type (ρ, δ), studied in Chapter IV. The presentation follows the line now widely adopted of first defining the operators by means of amplitudes, then proving (easily) the five basic theorems (pseudolocal character, continuity, transposition, composition, invariance under diffeomorphism), and only afterwards going to the symbolic calculus, by then a purely “algebraic” affair.
KeywordsVector Bundle Open Subset Pseudodifferential Operator Cotangent Bundle Principal Symbol
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