Clusters of exponential functions in the space of square integrable functions

TL;DR

This paper investigates the structure and limiting behavior of finite-dimensional subspaces formed by exponential functions within the space of square integrable functions, using expo-polynomials to describe their asymptotic positions.

Contribution

It introduces a novel analysis of the limiting positions of exponential function clusters in L2 spaces, characterized through expo-polynomials.

Findings

Describes the limiting positions of exponential function clusters.

Connects the asymptotic behavior to expo-polynomials.

Provides a framework for understanding exponential subspace limits.

Abstract

Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.