Some Conditions for Existence and Integrability of the Fourier Transform
Elijah Liflyand
Abstract
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions. The Fourier transform is calculated as an improper integral and the limit coincides with the Fourier transform in the distributional sense. The inverse Fourier formula is proved as well. Given are some applications of the result obtained.
Create a lesson
Related papers
Hilbert norms for graded algebras
Joachim Kupsch, Oleg G. Smolyanov
Equivariance and Imprimitivity for Discrete Hopf C*-Coactions
S. Kaliszewski, John Quigg
Distributional Asymptotic Expansions of Spectral Functions and of the Associated Green Kernels
R. Estrada, S. A. Fulling
On a class of stochastic differential equations used in quantum optics
Alberto Barchielli, Fabio Zucca
Cuntz-Krieger algebras for infinite matrices
Ruy Exel, Marcelo Laca
C*-Crossed Products by Twisted Inverse Semigroup Actions
Nandor Sieben