Explore: Fourier Integral Operators

Fourier integral operators have become an important tool in the theory of partial differential equations. The class of Fourier integral operators contains

The Fourier operator is the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform, and is a two-dimensional

In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input, and outputs another function that describes the extent

family of commuting operators). They are also special cases of pseudo-differential operators, and more generally Fourier integral operators. There are natural

Pseudodifferential Operators and Spectral Theory, Springer-Verlag 2001. ISBN 3-540-41195-X Francois Treves, Introduction to Pseudo Differential and Fourier Integral Operators

equation is called the Fourier integral theorem. Another way to state the theorem is that if R {\displaystyle R} is the flip operator i.e. ( R f ) ( x ) :=

method List of transforms List of operators List of Fourier-related transforms Nachbin's theorem Nonlocal operator Reproducing kernel Symbolic integration

All of these operators are bounded on Lp and satisfy weak-type (1, 1) estimates. A singular integral of convolution type is an operator T defined by convolution

ISBN 978-3-540-49937-4 The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators, Springer-Verlag, 2009 [1985], ISBN 978-3-642-00117-8 An

Plancherel theorem Peter–Weyl theorem Fourier integral operator Oscillatory integral operator Laplace operator Laplace equation Dirichlet problem Unit