arXiv subjects
Publications and source records attributed to Alp Arslan Kıraç.
In this article we consider Sturm-Liouville operator with $q\in W_{1}^{2}[0,1]$ and Dirichlet boundary conditions. We prove that if the set $\{(nπ)^{2}:n\in \mathbb{N}\}$ is a subset of the spectrum of the Sturm-Liouville operator with Dirichlet boundary conditions, then $q=0$ a.e.
An extension of the first eigenvalue-type Ambarzumyan's theorem are provided for the arbitrary self-adjoint Sturm-Liouville differential operators. The result makes a contribution to the Pöschel-Trubowitz inverse spectral theory as well.
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators $L_{t}(q)$ with $q\in L^{1}[0,1]$ and quasi-periodic boundary conditions, $t\in [0,2π)$, when there is not any additional condition on the potential $q$.
We consider Sturm-Liouville equation $y^{\prime\prime}+(λ-q)y=0$ where $q\in L^{1}[0,a]$. We obtain various conditions on the Fourier coefficients of q such that the periodic eigenvalues having the form given by Titchmarsh are asymptotically simple. Under these conditions, we give some asymptotic estimates for the spectral gaps.