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An Inversion Formula for the Weierstrass Transform
Canadian Journal of Mathematics, 1961The Weierstrass transform f(x) of a function ϕ(y) is defined by1.1wherewhenever this integral exists (7, p. 174). It is also known as the Gauss transform (11; 12). Its basic properties have been developed and studied in (7) and in particular it has been shown that the symbolic operatorwill invert this transform under suitable assumptions and with ...
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Inversion Formulas for a Cylindrical Radon Transform
SIAM Journal on Imaging Sciences, 2011In this paper we study the inversion of a generalized Radon transform that maps a function in three dimensional space to a family of cylindrical integrals. We derive local backprojection-type inversion formulas for this cylindrical Radon transform. Our inversion formulas can be implemented in a straightforward manner with $\mathcal{O}(\mathtt{N}^{4/3})$
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Scandinavian Actuarial Journal, 1983
Abstract Various inversion formulas in terms of characteristic functions, moments and real Laplace transforms are studied from the viewpoint of practical applicability. A new inversion integral in terms of the characteristic function for integer-valued variables and a new moment inversion formula for variables in the unit interval are given.
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Abstract Various inversion formulas in terms of characteristic functions, moments and real Laplace transforms are studied from the viewpoint of practical applicability. A new inversion integral in terms of the characteristic function for integer-valued variables and a new moment inversion formula for variables in the unit interval are given.
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Mathematical Proceedings of the Cambridge Philosophical Society, 1926
The extension of Mellin's inversion formula expressed by the equations has been considered by Fowler who shows that some form of Stieltjes integral is essential to Poincaré's proof of the necessity of the quantum hypothesis. Fowler confines his discussion to a restricted type of function φ (y) which is sufficient for the physical problem.
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The extension of Mellin's inversion formula expressed by the equations has been considered by Fowler who shows that some form of Stieltjes integral is essential to Poincaré's proof of the necessity of the quantum hypothesis. Fowler confines his discussion to a restricted type of function φ (y) which is sufficient for the physical problem.
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Inversion formula for the windowed linear canonical transform
Applicable Analysis, 2022Wenchang Sun, Yaoyao Han
exaly
On the inversion formula for probability densities
1997Let \(\varphi: \mathbb{R}^d \to\mathbb{C}\) be the characteristic function determined by a certain \(d\)-dimensional distribution function \(F:\mathbb{R}^d\to \langle 0,1 \rangle\subset \mathbb{R}\). Assuming that \(\varphi\) is square integrable, the author succeeds to derive from Lévy's inversion theorem a formula for the probability density of \(F\),
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An inversion formula for the Laplace transform
1992For real, right continuous and bounded functions \(f\) with Laplace transform \(\phi\) the inversion formula \[ f(x)= \lim_{\varepsilon\to +0} \lim_{\lambda\to \infty} {1\over \varepsilon} \sum_{\lambda x< k\leq \lambda(x+ \varepsilon)}(- 1)^ k {\lambda^ k\over k!} \phi^{(k)}(\lambda) \] is proved for \(x\geq 0\).
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