Recall the formula ( 2.54 ) for the quantization of a symbol \(a=a(x,\xi )\) , which is a polynomial in \(\xi \) : it defines the differential operator \(a(x,D)\) . When \(a\in S^m(\mathbb {R}^n;\mathbb {R}^n)\) is a general symbol, it defines a pseudodifferential operator. It is important for the development of the theory of ps.d.o.s to allow for symbols \(a=a(x,y,\xi )\in S^m(\mathbb {R}^n\times \mathbb {R}^n;\mathbb {R}^n)\) , as these naturally arise when studying adjoints and compositions.