The second regularized trace formula for the Sturm-Liouville operator

Abstract

In this paper, the second regularized trace formula for the differential operator with antiperiodic boundary conditions is obtained.

Second regularized trace of a differential operator of Sturm–Liouville type

“…Trace formulas for differential operators with operator coefficients are included in the works of Khalilova [27], Adıgüzelov [28], Adıgüzelov et al [29], Gül [30–33], Bayramov et al [34], Badalova [35], Karayel and Sezer [36], and Gül and Ceyhan [37]. The second regular trace formula of the Sturm–Liouville operator with inverse periodic boundary conditions and scalar coefficient is given in the study Akgun et al [38].…”

A Second Regularized Trace Formula for a Fourth Order Differential Operator

“…The trace formulae for differential operators with operator coefficients were studied in many works [10][11][12][13][14][15][16][17][18]. Recently a second regularized trace formula was obtained in [19] for the Sturm-Liouville operator with the antiperiodic boundary conditions.…”