New trace formula for the matrix Sturm-Liouville equation with eigenparameter dependent boundary conditions

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1. 1] Adiguzelov, E. E., Baykal, O. and Bayramov, A.: On the spectrum and regularized trace of the Sturm-Liouville problem with spectral parameter on the boundary condition and with the operator coefficient, International Journal of Differential Equations and Applications 2, 317–333 (2001). [2] Bayramoglu, M. and Sahinturk H.: Higher order regularized trace formula for the regular Sturm-Liouville equation contained spectral parameter in the boundary condition, Applied Mathematics and Computation 186, 1591–1599 (2007). [3] Carlson, R.: Large eigenvalues and trace formulas for matrix Sturm-Liouville problems, SIAM J. Math. Anal. 30, 949–962 (1999). [4] Carlson, R.: Eigenvalue estimates and trace formulas for the matrix Hill’s equation, J. Diff. Equations 167, 211–244 (2000). [5] Clark, S. and Gesztesy, F.: Eigenvalue estimates and trace formulas for the matrix Hill’s equation, J. Differential Equations 167, 211–244 (2000). [6] Dikii, L. A.: New method of computing approximate eigenvalues of the Sturm-Liouville problem, Dokl. Akad. Nauk SSSR 116, 12–14 (1957). [7] Faddeev, L. D.: On the expression for the trace of the difference of two singular differential operators of SturmLiouville type, Dokl. Akad. Nauk SSSR, 115, No. 5, 878–881 (1957). [8] Fulton, C. T.: Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburgh 77(A), 293–308 (1977). [9] Gelfand, I. M. and Levitan, B. M.: On a simple identity for eigenvalues of the differential operator of second order, Dokl. Akad. Nauk SSSR, 88, no. 4, 593–596 (1953). [10] Guliyev, N. J.: The regularized trace formula for the Sturm-Liouville equation with spectral parameter in the boundary conditions, Proc. Inst. Math. Natc. Acad. Sci. Azerb., 22, 99–102 (2005). [11] Rofe-Beketov F. S.: Self-adjoint extensions of differential operators in space of vector functions, Dokl. Akad. Nauk SSSR, 184, no. 5, 1034–1037 (1969). [12] Russakovskii E. M.: A matrix Sturm-Liouville problem with the eigenvalue parameter in the boundary conditions, Funct. Anal. Appl., 27, 73–74 (1993). [13] Sadovnichii, V. A. and Podol’skii, V. E.: Traces of differential operators, Differential Equations, 45, no. 4, 477–493 (2009). [14] Walter, J.: Regular eigenvalue problems with eigenvalue parameter in the boundary condition, Math. Z. 133, 301–312 (1973). [15] Yang, C. F.: New trace formulae for a quadratic pencil of the Schr¨odinger operator, Journal of Mathematical Physics, 51, 033506 (2