On the Boundary Value Problem for Discontinuous Sturm–Liouville Operator

On determination of discontinuous Sturm-Liouville operator fromWeyl function

“…Using the relations χ(τ n ) = 2τ n γ n µ n and ϕ(x, τ n ) = µ n u(x, τ n ) with µ n ̸ = 0 (see [2]), we find φ(τ n ) = −ϕ(0, τ n ) = −µ n . Then, it follows from this relation that…”

“…The spectral properties of the boundary value problem (1.1)-(1.3) are studied in [2]; namely, the integral representation of the solution of (1.1) with discontinuity conditions (1.2) is obtained and using this solution, the asymptotic formulas of the eigenvalues and eigenfunctions of this problem are investigated. Note that the constructed integral representation is not transformation operator, moreover; the kernel of this solution has a discontinuity along the line t = −a(x − ξ) + a, for ξ < a < π.…”

“…Theorem 1.1. [2] The integral representation of the solution f (x, τ ) of equation (1.1) with discontinuity conditions (1.2) satisfying the conditions f (0, τ ) = 1, f ′ (0, τ ) = iτ has the form:…”