A second regularized trace formula for a higher order differential operator

Abstract

In this paper, we obtain a second regularized trace formula on L2([0, π]; H) for a higher order self‐adjoint differential operator with unbounded operator‐valued coefficient, where H is a separable Hilbert space.

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].…”

“…The calculation of the second regularized trace formula of the Sturm–Liouville operator with operator coefficient introduced in Adıgüzelov et al [29] where the second regularized trace formula of the Sturm–Liouville operator with the bounded operator coefficient given by Dirichlet boundary conditions is given. In Gül and Ceyhan [37], second regularized trace formulas were found for a fourth‐order differential operator with a bounded operator coefficient given with symmetric boundary conditions, and in Gül [32], second regularized trace formula are found for a high‐order differential operator with unbounded operator coefficient given with symmetric boundary conditions. In addition, in Gül and Gill [39, 40], the first regularized trace formulas for differential operators with bounded and unbounded operator coefficients, respectively, are calculated on a separable Banach space.…”