Sinc Approximation in Strip

Abstract

In this chapter we develop methods to approximate analytic functions via Sinc series. Initially we obtain bounds on the error of approximation of functions that are analytic in the strip D _d of Equation (1.7.9), via the Sinc series derived in Section 1.9. The region D _d is a natural choice, since the modulus of the function sin(πz/h) which we employ to get the error of Sinc approximation is both large and nearly constant on the boundary of D _d . We also make an assumption on the growth of f in D _d , which has far-reaching consequences, and which enables us to replace the infinite Sinc series by a finite one.