Over the space of Schwartz functions, this operation is an endomorphism. This operation taken on the extension of a function is the subject of the Poisson summation formula, and Hankel generalized this operation to radial functions. This operation is unitary by Parseval's theorem, and the Cooley- Tukey algorithm is used to implement a "fast" version of this operation. Along with the Laplace transform, it is often used to analyze differential equations. Also useful in analog signal processing, FTP, name this transform that takes a function to its frequency domain, which is useful in decomposing waves and is named for a French mathematician.
Over the space of Schwartz functions, this operation is an endomorphism. This operation taken on the extension of a function is the subject of the Poisson summation formula, and Hankel generalized this operation to radial functions. This operation is unitary by Parseval's theorem, and the Cooley- Tukey algorithm is used to implement a "fast" version of this operation. Along with the Laplace transform, it is often used to analyze differential equations. Also useful in analog signal processing, FTP, name this transform that takes a function to its frequency domain, which is useful in decomposing waves and is named for a French mathematician.
Over the space of Schwartz functions, this operation is an endomorphism.
{Fourier Transform}