Universal truncation error upper bounds in irregular sampling restoration

TL;DR

This paper derives universal upper bounds for truncation errors in irregular sampling restoration sums for Bernstein function classes, applicable even when the decay rate of sampled functions is unknown, including multidimensional cases.

Contribution

It introduces universal truncation error bounds for irregular sampling in multidimensional settings without requiring decay rate knowledge.

Findings

Derived universal truncation error bounds for irregular sampling

Extended bounds to multidimensional sampling scenarios

Applicable to functions with unknown decay rates

Abstract

Universal (pointwise uniform and time shifted) truncation error upper bounds are presented in Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function class $B_{\pi,d}^q\,,\ q \ge 1,$ $d\in \mathbb N\,,$ when the sampled functions decay rate is unknown. The case of multidimensional irregular sampling is discussed.