Results 11 to 20 of about 3,323 (71)

Mellin and Widder–Lambert Transforms with Applications in the Salem Equivalence to the Riemann Hypothesis

Axioms
This 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, Jeetendrasingh Maan, Benito J. González   +2 more
doaj   +1 more source

Difference Sturm--Liouville problems in the imaginary direction

, 2011
We consider difference operators in $L^2$ on $\R$ of the form $$ L f(s)=p(s)f(s+i)+q(s) f(s)+r(s) f(s-i) ,$$ where $i$ is the imaginary unit. The domain of definiteness are functions holomorphic in a strip with some conditions of decreasing at infinity ...
Neretin, Yury
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Some New Applications of the Mellin Transform Involving the Lambert Transforms and Implications for the Riemann Hypothesis

Axioms
This work investigates the interplay between the Mellin transform and Lambert transforms to derive several novel results. In particular, we establish new inversion formulae for the Lambert transforms along with a Plancherel-type identity.
Hari M. Srivastava, Jeetendrasingh Maan, Emilio R. Negrín   +2 more
doaj   +1 more source

Lebedev's type index transforms with the modified Bessel functions [PDF]

, 2015
New index transforms of the Lebedev type are investigated. It involves the real part of the product of the modified Bessel functions as the kernel.
Yakubovich, Semyon
core   +1 more source

Tube domains and restrictions of minimal representations

, 2007
In this paper we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from $Sp(n,\mathbb{R})$ to $GL(n,\mathbb{R})$, and from SU(n,n) to $GL(n,\mathbb{C})$ respectively.
Seppanen, Henrik
core   +1 more source

Simple zeros of primitive Dirichlet $L$-functions and the asymptotic large sieve [PDF]

, 2013
Assuming the Generalized Riemann Hypothesis (GRH), we show using the asymptotic large sieve that 91% of the zeros of primitive Dirichlet $L$-functions are simple. This improves on earlier work of \"{O}zl\"{u}k which gives a proportion of at most 86%.
Chandee, Vorrapan, Lee, Yoonbok, Liu, Sheng-chi, Radziwiłł, Maksym   +3 more
core   +2 more sources

Generalized photon-added associated hypergeometric coherent states: characterization and relevant properties

, 2017
This paper presents the construction of a new set of generalized photon-added coherent states related to associated hypergeometric functions introduced in our previous work (Hounkonnou M N and Sodoga K, 2005, J. Phys. A: Math. Gen 38, 7851). These states
Aremua, I., Hounkonnou, M. N., Sodoga, K.   +2 more
core   +1 more source

Hitting densities for spectrally positive stable processes

, 2010
A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable L\'evy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute fractional ...
Simon, Thomas
core   +2 more sources

Index transforms with Weber type kernels

, 2018
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces.
Yakubovich, Semyon
core   +1 more source

On the Mellin transforms of powers of Hardy's function

, 2010
Various properties of the Mellin transform function $$ {\cal M}_k(s) := \int_1^\infty Z^k(x)x^{-s}dx $$ are investigated, where $$ Z(t) := \zeta(1/2+it){\bigl(\chi(1/2+it)\bigr)}^{-1/2}, \quad \zeta(s) = \chi(s)\zeta(1-s) $$ is Hardy's function and ...
Ivić, Aleksandar
core