inversion 
Finally, the problem of inversion of a multiplier will be analyzed for smooth functions that have a specified structure near their zeros.


Pointwise fourier inversion: A wave equation approach


When F is the characteristic function of [0, R2], this gives a representation for radial Fourier inversion.


A number of topics related to pointwise convergence or divergence of such inversion, as R → ∞, are studied in this article.


Pointwise fourier inversion and localisation in Rn


Calderón's formula associated with a differential operator on (0, ∞) and inversion of the generalized abel transform


We apply this result to derive a new inversion formula for the generalized Abel transform.


Pointwise Fourier inversion on tori and other compact manifolds


Approximate and explicit inversion formulas are obtained for a new class of exponential kplane transforms defined by where x∈?n, Θ is a kframe in ?n, 1≤k≤n1, μ∈?k is an arbitrary complex vector.


Similar inversion formulas are established for the accompanying transform where V is a real (n×k)matrix.


The proof relies on a family of inversion formulas for the SegalBargmann transform, which can be "tuned" to give the best estimates for a given value of p.


The Problem of the Pointwise Fourier Inversion for Piecewise Smooth Functions of Several Variables


We define a continuous Gabor transform for strong hypergroups and prove a Plancherel formula, an L2 inversion formula and an uncertainty principle for it.


In this article we analyze an inversion formula for helical computer tomography proposed earlier by the author.


Poisson Summation Formulas and Inversion Theorems for an Infinite Continuous Legendre Transform


We show that for the new Legendre transform variants of Poisson's formula and inversion theorems hold.


WaveletLike Transforms for Admissible SemiGroups; Inversion Formulas for Potentials and Radon Transforms


Inversion of the ShortTime Fourier Transform Using Riemannian Sums


The inversion formula for the shorttime Fourier transform is usually considered in the weak sense, or only for specific combinations of window functions and function spaces such as L2 and modulation spaces.


This result combined with the matrix analog of the Hilbert transform leads to variety of new explicit inversion formulas for the Radon transform of functions of matrix argument.

