On the Eigenvalues of the Operator $(Tf)(t)=f(t)-\sum_{n=0}^\infty\frac{f^{(n)}(0)}{n!}t^n$

TL;DR

This paper determines the eigenvalues of a specific linear operator involving derivatives and power series, showing that only 0 and 1 are possible eigenvalues.

Contribution

It proves that the only eigenvalues of the operator are 0 and 1, providing a complete spectral characterization.

Findings

Eigenvalues of the operator are only 0 and 1.

The spectral properties of the operator are fully characterized.

The result clarifies the operator's behavior in functional analysis.

Abstract

We show that the only eigenvalues of this operator are 0 and 1.