# On the trace formula for higher-order ODO

## TL;DR

This paper derives a trace formula for higher-order differential operators with measure perturbations, revealing a new term for even orders greater than or equal to four, advancing spectral analysis techniques.

## Contribution

It introduces a novel trace formula for higher-order ODOs with measure perturbations, including a new term for even orders n ≥ 4.

## Key findings

- Derived a first-order trace formula for higher-order ODOs.
- Discovered a new term in the trace formula for even orders n ≥ 4.
- Extended spectral analysis methods for differential operators.

## Abstract

A first order trace formula is obtained for a higher-order differential operator on a segment in the case where the perturbation is an operator of multiplication by a finite complex-valued measure. For the operators of even order $n\ge4$ a new term in the final formula is discovered.