On root mean square approximation by exponential functions

TL;DR

This paper investigates the problem of approximating square integrable functions using exponential functions, solving the linear case and exploring specific examples for the nonlinear case.

Contribution

It provides a solution to the linear approximation problem and analyzes particular examples of the nonlinear problem in root mean square approximation.

Findings

Linear approximation problem solved.

Nonlinear problem analyzed in specific cases.

Insights into exponential function approximation methods.

Abstract

The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is solved. Then the nonlinear problem is studied in some particular example.