%0 Journal Article
%T Exponential Cauchy Transforms
%A El-Bachir Yallaoui
%J Journal of Interpolation and Approximation in Scientific Computing
%D 2012
%I International Scientific Publications and Consulting Services (ISPACS)
%R 10.5899/2012/jiasc-00005
%X 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( xz ight) ight] dmu(x) where $Kleft( z ight) =left( 1-z ight) ^{-1}$ 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 $H^{p}$.
%K Exponential Cauchy transforms
%K Laguerre polynomial
%K Turan's inequality
%U http://www.ispacs.com/journals/jiasc/2012/jiasc-00005/article.pdf