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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 k-plane transforms defined by where x∈?n, Θ is a k-frame in ?n, 1≤k≤n-1, 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 Segal-Bargmann 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.
      
Wavelet-Like Transforms for Admissible Semi-Groups; Inversion Formulas for Potentials and Radon Transforms
      
Inversion of the Short-Time Fourier Transform Using Riemannian Sums
      
The inversion formula for the short-time 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.
      
 

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