Eigenvalue Asymptotics for Sturm–liouville Operators with Singular Potentials
نویسنده
چکیده
We derive eigenvalue asymptotics for Sturm–Liouville operators with singular complex-valued potentials from the space W 2 (0, 1), α ∈ [0, 1], and Dirichlet or Neumann–Dirichlet boundary conditions. We also give application of the obtained results to the inverse spectral problem of recovering the potential by these two spectra.
منابع مشابه
Inverse Eigenvalue Problems for Nonlocal Sturm–liouville Operators
We solve the inverse spectral problem for a class of Sturm–Liouville operators with singular nonlocal potentials and nonlocal boundary conditions.
متن کاملEigenfunction expansion in the singular case for q-Sturm-Liouville operators
In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.
متن کاملOn inverse problem for singular Sturm-Liouville operator with discontinuity conditions
In this study, properties of spectral characteristic are investigated for singular Sturm-Liouville operators in the case where an eigen parameter not only appears in the differential equation but is also linearly contained in the jump conditions. Also Weyl function for considering operator has been defined and the theorems which related to uniqueness of solution of inverse proble...
متن کاملInverse Spectral Problems for Sturm-liouville Operators with Singular Potentials, Iv. Potentials in the Sobolev Space Scale
We solve the inverse spectral problems for the class of Sturm–Liouville operators with singular real-valued potentials from the Sobolev space W s−1 2 (0, 1), s ∈ [0, 1]. The potential is recovered from two spectra or from the spectrum and norming constants. Necessary and sufficient conditions on the spectral data to correspond to the potential in W s−1 2 (0, 1) are established.
متن کاملSturm-Liouville Fuzzy Problem with Fuzzy Eigenvalue Parameter
This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.
متن کامل