Geodesic
The first regularized trace for the two-fold differentiation operator in~a~punctured segment
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 626-633

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There are found the formulas of the first regularized trace (of the type of abstract Gel'fand–Levitan formula) of the two-fold differentiation operator in a punctured segment. Proof of the main result is given by the method of contour integration with corrections of the analytic perturbation theory. Some well-known trace formulas are generalized.
Keywords: Differential operator, First Regularized Trace, Eigenvalue, Characteristic function. 
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     author = {M. E. Akhymbek and D. B. Nurakhmetov},
     title = {The first regularized trace for the two-fold differentiation operator in~a~punctured segment},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {626--633},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a63/}
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M. E. Akhymbek; D. B. Nurakhmetov. The first regularized trace for the two-fold differentiation operator in~a~punctured segment. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 626-633. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a63/