Sinc approximation of algebraically decaying functions
For researchers in numerical analysis and approximation theory, this work incrementally extends existing sinc interpolation methods to a new class of functions.
The paper extends sinc interpolation to algebraically decaying functions, providing two types of error estimates: one for a wide class of functions with algebraic decay on R, and another for functions whose decay order can be estimated in a horizontal strip of the complex plane. Numerical examples are given.
An extension of sinc interpolation on $\mathbb{R}$ to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we establish two types of error estimates. First covers a wider class of functions with the algebraic order of decay on $\mathbb{R}$. The second type of error estimates governs the case when the order of function's decay can be estimated everywhere in the horizontal strip of complex plane around $\mathbb{R}$. The numerical examples are provided.