Trace formula for fourth order operators on the circle
Andrey Badanin, Evgeny Korotyaev
TL;DR
This paper derives a trace formula for a fourth order differential operator on the circle, extending the classical trace formula known for the Hill operator to higher order operators.
Contribution
The paper introduces a trace formula for fourth order operators on the circle, expanding the theoretical framework established for second order operators.
Findings
Derived the trace formula for the fourth order operator on the circle.
Showed similarities between the new formula and the classical Hill operator trace formula.
Extended the mathematical understanding of spectral properties of higher order operators.
Abstract
We determine the trace formula for the fourth order operator on the circle. This formula is similar to the famous trace formula for the Hill operator obtained by Dubrovin, Its-Matveev and McKean-van Moerbeke.
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