M. E. Akhymbek, D. B. Nurakhmetov, “The first regularized trace for the two-fold differentiation operator in a punctured segment”, Sib. Èlektron. Mat. Izv., 2014, Volume 11,Pages <nobr>626

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Differentical equations, dynamical systems and optimal control

The first regularized trace for the two-fold differentiation operator in a punctured segment

M. E. Akhymbek, D. B. Nurakhmetov

Al-Farabi Kazakh National University

Abstract: 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.

UDC: 517.984

MSC: 34B05,34В24,34L10

Received April 29, 2013, published August 30, 2014