Inverse spectral problems for non-selfadjoint second-order differential operators with Dirichlet boundary conditions

[[abstract]]We study the inverse problem for non-selfadjoint Sturm-Liouville operators on a finite interval with possibly multiple spectra. We prove the uniqueness theorem and obtain constructive procedures for solving the inverse problem along with the necessary and sufficient conditions of its solvability and also prove the stability of the solution.[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]電子版[[countrycodes]]DE

Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval

[[abstract]]In this paper, the vectorial Sturm-Liouville operator L Q =−d 2 dx 2 +Q(x) is considered, where Q(x) is an integrable m×m matrix-valued function defined on the interval [0,π] . The authors prove that m 2 +1 characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely. In particular, if Q(x) is real symmetric, then m(m+1) 2 +1 characteristic functions can determine the potential function uniquely. Moreover, if only the spectral data of self-adjoint problems are considered, then m 2 +1 spectral data can determine Q(x) uniquely.[[notice]]補正完畢[[incitationindex]]SCI[[cooperationtype]]國外[[booktype]]電子

Inverse problems for Sturm-Liouville equations with boundary conditions linearly dependent on the spectral parameter from partial information

[[abstract]]Abstract.In this paper, we study the inverse spectral problems for Sturm–Liouville equations with boundary conditions linearly dependent on the spectral parameter and show that the potential of such problem can be uniquely determined from partial information on the potential and parts of two spectra, or alternatively, from partial information on the potential and a subset of pairs of eigenvalues and the normalization constants of the corresponding eigenvalues.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]DE

Inverse nodal and inverse spectral problems for discontinuous boundary value problems

[[abstract]]Inverse nodal and inverse spectral problems are studied for second-order differential operators on a finite interval with discontinuity conditions inside the interval. Uniqueness theorems are proved, and a constructive procedure for the solution is provided.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]US

On Hochstadt-Lieberman Theorem For Sturm-Liouville Operators

[[abstract]]The inverse spectral problem of the Sturm-Liouville operator Lq = -d2/dx2 +q(x) is considered, where q(x) is an integrable function on (0,1). Some analogies of the Hochstadt-Lieberman Theorem for SturmLiouville operators are proved.[[notice]]補正完畢[[booktype]]紙

Some inverse problems on Jacobi matrices

[[abstract]]In this paper, we use a relation between products of matrices on M2 (R[x]) and Jacobi matrices to study some inverse problems on Jacobi matrices, including uniqueness and existence theorems.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]GB

On the reconstruction of a boundary value problem from incomplete nodal data

. In this paper, the reconstruction of a differential operator from incomplete spectral characteristics is concerned. We prove that coefficients of a second-order differential equation with the eigen-parameter appearing at the right-end boundary condition can be uniquely determined from incomplete nodal data. The new results in this paper are unlike to the known results for the classical Sturm-Liouville operator in [21].補正完畢DE