Fourier integral operator
Fourier integral operator 2 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia In mathematical analysis , Fourier integral operators have become an important tool in the theory of partial differential equations . The class of Fourier integral operators contains differential operators as well as classical integral operators as special cases. A Fourier integral operator � is given by: ( � � ) ( � ) = ∫ � � � 2 � � Φ ( � , � ) � ( � , � ) � ^ ( � ) � � where � ^ denotes the Fourier transform of � , � ( � , � ) is a standard symbol which is compactly supported in � and Φ is real valued and homogeneous of degree 1 in � . It is also necessary to require that det ( ∂ 2 Φ ∂ � � ∂ � � ) ≠ 0 on the support of a. Under these conditions, if a is of order zero, it is possible to show...