arXiv subjects
Publications and source records attributed to Faruk Abi-Khuzam.
We illustrate the interplay between certain discrete and continuous problems, by presenting a method for the study of the asymptotics of a divergent sequence, through consideration of the asymptotics of its continuous analogue
For $α>β-1>0$, we obtain two sided inequalities for the moment integral $I(α,β)= \int_{\mathbb{R}} |x|^{-β}|\sin x|^αdx$. These are then used to give the exact asymptotic behavior of the integral as $α\to \infty$. The case $I(α,α)$ corresponds to the asymptotics of Ball's inequality, and $I(α,[α]-1)$ corresponds to a kind of novel "oscillatory" behavior.
We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then characterize meromorphic functions admitting a harmonic star function.