The fourier transformation and inversion formulas for S u 0 for all u

1970 ◽  
pp. 139-201
Author(s):  
Allan J. Silberger
Keyword(s):  
Fourier Transformation ◽  
Inversion Formulas ◽  
And Inversion

scholarly journals Ranges and Inversion Formulas for Spherical Mean Operator and Its Dual

1995 ◽  
Vol 196 (3) ◽  
pp. 861-884 ◽  
Author(s):  
M.M. Nessibi ◽  
L.T. Rachdi ◽  
K. Trimeche
Keyword(s):  
Spherical Mean Operator ◽  
Inversion Formulas ◽  
Spherical Mean ◽  
And Inversion

scholarly journals Besov-Hankel norms in terms of the continuous Bessel wavelet transform

2021 ◽  
Author(s):  
Ashish Pathak ◽  
Dileep Kumar
Keyword(s):  
Wavelet Transform ◽  
Wavelet Coefficient ◽  
Inversion Formulas ◽  
And Inversion

Using the theory of continuous Bessel wavelet transform in $L^2 (\mathbb{R})$-spaces, we established the Parseval and inversion formulas for the $L^{p,\sigma}(\mathbb{R}^+)$- spaces. We investigate continuity and boundedness properties of Bessel wavelet transform in Besov-Hankel spaces. Our main results: are the characterization of Besov-Hankel spaces by using continuous Bessel wavelet coefficient.

A brief comparison of some Kirchhoff integral formulas for migration and inversion

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1164-1169 ◽  
Author(s):  
Paul Docherty
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Reflection Coefficients ◽  
Acoustic Wave Equation ◽  
Inversion Formulas ◽  
Kirchhoff Migration ◽  
Integral Formulas ◽  
The One ◽  
And Inversion ◽  
Kirchhoff Integral

Kirchhoff migration has traditionally been viewed as an imaging procedure. Usually, few claims are made regarding the amplitudes in the imaged section. In recent years, a number of inversion formulas, similar in form to those of Kirchhoff migration, have been proposed. A Kirchhoff‐type inversion produces not only an image but also an estimate of velocity variations, or perhaps reflection coefficients. The estimate is obtained from the peak amplitudes in the image. In this paper prestack Kirchhoff migration and inversion formulas for the one‐parameter acoustic wave equation are compared. Following a heuristic approach based on the imaging principle, a migration formula is derived which turns out to be identical to one proposed by Bleistein for inversion. Prestack Kirchhoff migration and inversion are, thus, seen to be the same—both in terms of the image produced and the peak amplitudes of the output.

scholarly journals Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds

2019 ◽  
Vol 20 (2) ◽  
pp. 1129 ◽  
Author(s):  
Feng Qi ◽  
Da-Wei Niu ◽  
Dongkyu Lim
Keyword(s):  
Chebyshev Polynomials ◽  
Inversion Formulas ◽  
And Inversion

scholarly journals DEFORMATIONS AND INVERSION FORMULAS FOR FORMAL AUTOMORPHISMS IN NONCOMMUTATIVE VARIABLES

2007 ◽  
Vol 17 (02) ◽  
pp. 261-288 ◽  
Author(s):  
WENHUA ZHAO
Keyword(s):  
Inversion Formula ◽  
Integral Domain ◽  
Rooted Trees ◽  
Cauchy Problems ◽  
Inversion Formulas ◽  
Formal Parameter ◽  
Free Variables ◽  
And Inversion ◽  
Special Case

Let z = (z1, z2,…, zn) be noncommutative free variables and t a formal parameter which commutes with z. Let k be any unital integral domain of any characteristic and Ft(z) = z - Ht(z) with Ht(z) ∈ k[[t]]〈〈z〉〉×n and the order o(Ht(z))≥ 2. Note that Ft(z) can be viewed as a deformation of the formal map F(z):= z - Ht=1(z) when it makes sense (for example, when Ht(z) ∈ k[t]〈〈z〉〉×n). The inverse map Gt(z) of Ft(z) can always be written as Gt(z) = z+Mt(z) with Mt(z) ∈ k[[t]]〈〈z〉〉×n and o(Mt(z)) ≥ 2. In this paper, we first derive the PDEs satisfied by Mt(z) and u(Ft), u(Gt) ∈ k[[t]]〈〈z〉〉 with u(z) ∈ k〈〈z〉〉 in the general case as well as in the special case when Ht(z) = tH(z) for some H(z) ∈ k〈〈z〉〉×n. We also show that the elements above are actually characterized by certain Cauchy problems of these PDEs. Secondly, we apply the derived PDEs to prove a recurrent inversion formula for formal maps in noncommutative variables. Finally, for the case char. k = 0, we derive an expansion inversion formula by the planar binary rooted trees.

A sample-path approach to Palm probabilities

1994 ◽  
Vol 31 (2) ◽  
pp. 430-437
Author(s):  
Shaler Stidham
Keyword(s):  
Path Analysis ◽  
Function Space ◽  
Point Process ◽  
Sample Path ◽  
Probability Measures ◽  
Sample Path Analysis ◽  
Inversion Formulas ◽  
One Dimensional ◽  
And Inversion ◽  
Palm Probabilities

Previous papers have established sample-path versions of relations between marginal time-stationary and event-stationary (Palm) state probabilities for a process with an imbedded point process. This paper extends the use of sample-path analysis to provide relations between frequencies for arbitrary (measurable) sets in function space, rather than just marginal (one-dimensional) frequencies. We define sample-path analogues of the time-stationary and event-stationary (Palm) probability measures for a process with an imbedded point process, and then derive sample-path versions of the Palm transformation and inversion formulas.

Crofton's function and inversion formulas in real integral geometry

1991 ◽  
Vol 25 (1) ◽  
pp. 1-5 ◽  
Author(s):  
I. M. Gel'fand ◽  
M. I. Graev
Keyword(s):  
Integral Geometry ◽  
Inversion Formulas ◽  
And Inversion
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