The first regularized trace for the twofold differentiation operator in a punctured segment
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.