Reamrk 5.2.

Let

where m 1 , m 2 , … , m r ∈ ℝ , and assume that there exist positive constants C 1 , C 2 , … , C r satisfying the conditions | ∂ x α ⁡ e i ⁢ Φ l ⁢ ( x , ξ l ) | ≤ C l for every multi-index α and 1 ≤ l ≤ r . Let Φ i , 1 ≤ i ≤ r , be scalar-valued functions which are linear in the second variable so they take the form of c i ⁢ ξ i for each 1 ≤ i ≤ r , where c 1 , c 2 , … , c r are real numbers. Then the Fourier integral operator T σ is well defined.