First Regularized Trace of the Limit Assignment of Sturm-Liouville Type with Two Constant Delays

We observe spectral assignment D(2)y = lambda y defined by -y '' (x) + q(1)(x)y(x - tau(1)) + q(2)(x)y(x - tau(2)) = lambda y(x), = z(2) (1) q(1)(x), q(2)(x) is an element of L-1[0, pi], tau(1), tau(2) is an element of (0, pi) y(x - tau(1)) equivalent to 0, x is an element of (0, tau(1)], tau(1) = k(0)tau(2) (2) y(pi) = 0 (3) In this paper, we construct a solution y(x, z) which satisfies (1) and (2), and then (3) is used to construct the characteristic function F(z), z is an element of C. Then the asymptotics of eigenvalues of the operator D-2 is constructed. Finally, the first regularized trace is calculated.