Journal of Spectral Theory


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Volume 4, Issue 2, 2014, pp. 365–389
DOI: 10.4171/JST/73

Published online: 2014-07-13

The Tamarkin equiconvergence theorem and a first-order trace formula for regular differential operators revisited

Alexander I. Nazarov[1], Dmitry M. Stolyarov[2] and Pavel B. Zatitskiy[3]

(1) St. Petersburg State University, Russian Federation
(2) St. Petersburg State University, Russian Federation
(3) St. Petersburg State University, Russian Federation

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.

Keywords: Equiconvergence, regularized traces

Nazarov Alexander, Stolyarov Dmitry, Zatitskiy Pavel: The Tamarkin equiconvergence theorem and a first-order trace formula for regular differential operators revisited. J. Spectr. Theory 4 (2014), 365-389. doi: 10.4171/JST/73