Rational function approximation of Hardy space on half strip

Abstract

ABSTRACTIn this paper, through appropriate rational approximation, we prove that a function f in , with particular interest in the index range can be decomposed into a sum in the sense of , where is a half strip domain in the complex plane, g and h are the non-tangential limits of functions in and , respectively. For the case we show that a rational function in can be decomposed into a sum of rational functions in and .