On formula of regularized traces II
Alexander I. Nazarov, Dmitriy M. Stolyarov, Pavel B. Zatitskiy
TL;DR
This paper derives a simple formula for the first-order trace of a regular differential operator on a segment, perturbed by a multiplication operator, using an improved Tamarkin equiconvergence theorem.
Contribution
It provides a new, simplified formula for the trace of differential operators under perturbation, enhancing previous theoretical results.
Findings
Derived a simple trace formula for differential operators
Improved the Tamarkin equiconvergence theorem
Enhanced understanding of operator perturbations
Abstract
We obtain a simple formula for the first-order trace of a regular differential operator on a segment perturbated by a multiplication operator. The main analytic ingredient of the proof is an improvement of the Tamarkin equiconvergence theorem.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Differential Equations and Boundary Problems · Spectral Theory in Mathematical Physics