Results 261 to 270 of about 33,049 (300)

Chen’s inversion formula

Physical Review A, 1990
Nan-xian Chen [Phys. Rev. Lett. 64, 1193 (1990)] has generalized a formula of classical algebraic number theory to continuous variables and noted some useful consequences of the generalization. We present an alternative view of this analysis, based on the Mellin transformation and Riemann's \ensuremath{\zeta} function.
, Hughes, , Frankel, , Ninham
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On the order of summability of the Fourier inversion formula [PDF]

Analysis in Theory and Applications, 2010
In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related.
Jasson Vindas, Ricardo Estrada, Vindas Jasson   +2 more
exaly   +3 more sources

Arithmetical Inversion Formulas

Canadian Journal of Mathematics, 1960
Let n and r be integers, r positive, and define the coreγ(r) of r to be the product of the distinct prime factors of r (γ(1) = 1). Let f(n,r) be a complex-valued, arithmetical function of n and r. If for all n,f﹛n,r) = f((n,r), r) then f(n, r) is called an even function (mod r), and if f(n,r) = f(γ(n, r), r) for all n, γ(n, r) = γ((n, r)), then f(n, r)
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Arithmetical Functions and Inversion Formulae

Journal of the London Mathematical Society, 1974
For a fixed integer \(N\ge 2\) let \(\nu_N(m) = 1\) if \(m\) is an \(N\)-th power and \(0\) otherwise, and let \(\lambda_N(n)= \sum_{m\mid n} \mu(n/m)\nu_N(m)\). The authors derive the following inversion formulae, in which \(T\) runs through the \(N\)-free integers: \[ f(n)= \sum_{T\mid n} g(n/T) \Leftrightarrow g(n) = \sum_{d\mid n} \lambda(d)f(n/d),
Evelyn, C. J. A., Heath-Brown, D.
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Ramanujan’s hyperelliptic inversion formula

The Ramanujan Journal, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some Finite Inversion Formulae

The Mathematical Gazette, 1962
In a great many problems in probability, one is given one set of quantities X j expressed in terms of a second set of quantities Y k
Stanton, R. G., Sprott, D. A.
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Inversion techniques and reciprocal formulae

International Journal of Computer Applications in Technology, 2012
Combinatorics has an important role in the development of computer science. Combinatorial identity which attracts numerous mathematicians is absolutely an important branch of it. As the effective tools, all kinds of inversion techniques are often used to prove known results and find new identities.
Chuanan Wei, Dianxuan Gong
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Algorithm study of Collins formula and inverse Collins formula

Applied Optics, 2007
In the study of a diffraction field of a light wave passing through a symmetrical paraxial optical system, the Collins formula and its inverse are convenient for calculation. The algorithm study of the Collins formula demonstrates that both a single fast Fourier transform algorithm and a double fast Fourier transform algorithm can be used in ...
Junchang, Li, Chongguang, Li
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A Direct Inversion Formula for SFT

Sankhya A, 2014
The subject of the paper is the stochastic Fourier transformation, for short SFT. The paper is a continuation of the author's previous works [C. R. Acad. Sci., Paris, Sér. A 288, 359--362 (1979; Zbl 0397.60047); Japan J. Appl. Math. 2, 229--240 (1985; Zbl 0616.60056); in: Patterns and waves.
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An Inversion Formula for the Weierstrass Transform

Canadian Journal of Mathematics, 1961
The 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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