Remarks on the inverse spectral theory for singularly perturbed operators
نویسندگان
چکیده
Let A be an unbounded from above self-adjoint operator in a separable Hilbert space H and EA(·) its spectral measure. We discuss the inverse spectral problem for singular perturbations à of A (à and A coincide on a dense set in H). We show that for any a ∈ R there exists a singular perturbation à of A such that à and A coincide in the subspace EA((−∞, a))H and simultaneously à has an additional spectral branch on (−∞, a) of an arbitrary type. In particular, à may possess the prescribed spectral properties in the resolvent set of the operator A on the left from a point a. Moreover, for an arbitrary self-adjoint operator T in H there exists à such that T is unitary equivalent to a part of à acting in an appropriate invariant subspace. 2000 Mathematics Subject Classification: 47A10, 47A55.
منابع مشابه
Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملA hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer
The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...
متن کاملAn efficient numerical method for singularly perturbed second order ordinary differential equation
In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
متن کاملInverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions
In this paper, we study the inverse problem for Dirac differential operators with discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...
متن کامل