Extreme and exposed points of shift-invariant spaces generated by Gaussian kernel and hyperbolic secant

TL;DR

This paper characterizes the extreme and exposed points of the unit ball in specific shift-invariant spaces generated by Gaussian and hyperbolic secant functions, advancing understanding of their geometric structure.

Contribution

It provides a novel characterization of extreme and exposed points in shift-invariant spaces generated by Gaussian and hyperbolic secant functions.

Findings

Identifies extreme points in Gaussian-generated shift-invariant spaces.

Characterizes exposed points in hyperbolic secant-generated quasi shift-invariant spaces.

Enhances understanding of the geometric structure of these function spaces.

Abstract

We characterize the extreme and exposed points of the unit ball (with respect to the $L^1$-norm) in the shift-invariant space generated by the Gaussian function, as well as in the quasi shift-invariant space generated by the hyperbolic secant.