Results 1 to 10 of about 172,616 (81)
A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces [PDF]
Mathematische Nachrichten, 2017 Here we give a new approach to the Paley--Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of "polar-analytic function" in the Mellin setting and Mellin--Bernstein spaces.
Carlo Bardaro +2 more
exaly +1 more source
On the Relation between Lambert W-Function and Generalized Hypergeometric Functions
Stats, 2022 In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambert W-
Pushpa Narayan Rathie +1 more
doaj +1 more source
Estimates and properties of certain q-Mellin transform on generalized q-calculus theory
Advances in Difference Equations, 2021 This paper deals with the generalized q-theory of the q-Mellin transform and its certain properties in a set of q-generalized functions. Some related q-equivalence relations, q-quotients of sequences, q-convergence definitions, and q-delta sequences are ...
Shrideh Al-Omari
doaj +1 more source
Advances in Difference Equations, 2020 In this article, we investigate the so-called Inayat integral operator T p , q m , n $T_{p,q}^{m,n}$ , p , q , m , n ∈ Z $p,q,m,n\in \mathbb{Z}$ , 1 ≤ m ≤ q $1\leq m\leq q$ , 0 ≤ n ≤ p $0\leq n\leq p $ , on classes of generalized integrable functions. We
Shrideh Khalaf Al-Omari
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A Note on the Axisymmetric Diffusion equation [PDF]
The ANZIAM Journal, Volume 63, Issue 3, July 2021, pp. 333--341, 2020 We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for $u(r,t)$ as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as rapidly ...
arxiv +1 more source
Celestial Mellin Amplitude [PDF]
, 2022 Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient in connecting the two sides is the celestial amplitude, which is given by the Mellin transform of momentum space scattering amplitude in energy.
arxiv +1 more source
International Journal of Mathematics and Mathematical Sciences, 1988 A formula of inversion is established for an integral transform whose kernel is the Bessel function Ju(kr) where r varies over the finite interval (0,a) and the order u is taken to be the eigenvalue parameter.
D. Naylor
doaj +1 more source
To Multidimensional Mellin Analysis: Besov spaces, $K$-functor, approximations, frames [PDF]
arXiv, 2022 In the setting of the multidimensional Mellin analysis we introduce moduli of continuity and use them to define Besov-Mellin spaces. We prove that Besov-Mellin spaces are the interpolation spaces (in the sense of J.Peetre) between two Sobolev-Mellin spaces.
arxiv
A Simple Proof of Siegel's Theorem Using Mellin Transform [PDF]
arXiv, 2022 In this paper, we present a simple analytic proof of Siegel's theorem that concerns the lower bound of $L(1,\chi)$ for primitive quadratic $\chi$. Our new method compares an elementary lower bound with an analytic upper bound obtained by the inverse Mellin transform of $\Gamma(s)$.
arxiv
AxiomsThis paper presents a comprehensive study of Plancherel’s theorem and inversion formulae for the Widder–Lambert transform, extending its scope to Lebesgue integrable functions, compactly supported distributions, and regular distributions with compact ...
Emilio R. Negrín +2 more
doaj +1 more source