Inverse Problems for Dirac Operator with Boundary Conditions İnvolving A Herglotz-Nevanlinna function

Abstract

Abstract. In this paper, we deal with the inverse problems for Dirac operator with rationally eigenvalue dependent boundary condition and linearly eigenvalue dependent jump conditions. We prove that whenthen only one spectrum excluding a finite number of eigenvalues is sufficient to determine ) (x Q on the interval   0,1 and the other coefficients of the problem. Moreover, it is shown that ) (x Q is uniquely determined by the classical spectral data, i.e., eigenvalues and normalising numbers.

Solving an inverse nodal problem with Herglotz–Nevanlinna functions in boundary conditions using the second‐kind Chebyshev wavelets method

“…However, it supplies a tool for handling HN functions. HN functions in one variable are used in various contexts, for example, in spectral theory with extensions of symmetric operators, in systems theory, 11 in inverse problems for Dirac operator, 12 and in some problems related to Hilbert transform 13 . Now let us make some evaluations about the method we use while solving the problem we are dealing with.…”