Academic Journals Database
Disseminating quality controlled scientific knowledge

Exponential Cauchy Transforms

Author(s): El-Bachir Yallaoui

Journal: Journal of Interpolation and Approximation in Scientific Computing
ISSN 2194-3907

Volume: 2012;
Start page: 1;
Date: 2012;
VIEW PDF   PDF DOWNLOAD PDF   Download PDF Original page

Keywords: Exponential Cauchy transforms | Laguerre polynomial | Turan's inequality

In this article, we introduce a new class of analytic functions of the unit disc $mathbf{D}$ namely the Exponential Cauchy Transforms $mathbf{{K}_{e}}$ defined by f(z)= {displaystyleint_{mathbf{T}}} expleft[ Kleft( xzight) ight] dmu(x) where $Kleft( zight) =left( 1-zight) ^{-1}$ is classical Cauchy kernel and $mu(x)$ is a complex Borel measures and $x$ belongs to the unit circle $mathbf{T}$ . We use Laguerre polynomials to explore the coefficients of the Taylor expansions of the kernel and Peron's formula to study the asymptotic behavior of the Taylor coefficients. Finally we investigate relationships between our new class $mathbf{{K}_{e}}$, the classical Cauchy space $mathbf{K}$ and the Hardy spaces $H^{p}$.
Why do you need a reservation system?      Save time & money - Smart Internet Solutions