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Regularized traces of singular differential operators. (English. Russian original) Zbl 1190.47053

Dokl. Math. 80, No. 1, 550-554 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 427, No. 4, 461-465 (2009).
In the space \(L^2[0,\infty)\), a higher order selfadjoint differential operator on the positive half-line is explored. It is assumed that the considered operator is lower semibounded. The authors investigate the variation of the regularized trace under perturbation by the operator of multiplication by a real function.

MSC:

47E05 General theory of ordinary differential operators
47A10 Spectrum, resolvent
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References:

[1] M. G. Gasymov, Dokl. Akad. Nauk SSSR 150, 1202–1205 (1963).
[2] A. G. Kostyuchenko, Doctoral Dissertation in Mathematics and Physics (MGU, Moscow, 1966).
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