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Traces of operators. (English. Russian original) Zbl 1157.47013
Russ. Math. Surv. 61, No. 5, 885-953 (2006); translation from Usp. Mat. Nauk 61, No. 5, 89-156 (2006).
In this paper, the authors give a survey of traces of operators. It is devoted to regularized traces of ordinary differential operators and the general theory is presented. Moreover, in appendices the following problems are considered: the spectral function and the Krein formula, zeta function, theta function, noncommutative residue and spectral asymmetry, index theory for linear operators, approximate calculation of the first eigenvalues, and unsolved problems.

MSC:
47A55 Perturbation theory of linear operators
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
47A10 Spectrum, resolvent
34B24 Sturm-Liouville theory
40G10 Abel, Borel and power series methods
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