Interpolation and Sampling with Exponential Splines of Real Order

TL;DR

This paper introduces fundamental cardinal exponential B-splines of positive real order, establishes their existence under certain conditions, and presents a sampling theorem for these splines, expanding the mathematical framework for exponential spline analysis.

Contribution

It provides the first construction and existence proof of exponential B-splines of real order and a corresponding sampling theorem, broadening spline theory beyond integer orders.

Findings

Existence of exponential B-splines of positive real order established

Construction method for these splines implemented

Sampling theorem for exponential B-splines proved

Abstract

The existence of fundamental cardinal exponential B-splines of positive real order $\sigma$ is established subject to two conditions on $\sigma$ and their construction is implemented. A sampling result for these fundamental cardinal exponential B-splines is also presented.