arXiv subjects

Avetik Pahlevanyan

Publications and source records attributed to Avetik Pahlevanyan.

4 recordsLinked to original sources

arXiv2017

On the constructive solution of an inverse Sturm-Liouville problem

The necessary and sufficient conditions are found for the two sequences $\left\{μ_n \right\}_{n=0}^{\infty}$ and $\left\{a_n \right\}_{n=0}^{\infty}$ to be the spectrum and the norming constants respectively, for a boundary value problem $-y'' + q \left( x \right) y = μy,$ $y \left(0\right)=0,$ $y\left( π\right)\cos β+ y'\left( π\right)\sin β= 0,$ $β\in \left( 0, π\right),$ with $q \in L_{\mathbb{R}}^1 \left[0, π\right].$

math.SP↗

arXiv2016

On the norming constants of the Sturm-Liouville problem

We derive new asymptotic formulae for the norming constants of Sturm-Liouville problem with summable potentials, which generalize and make more precise previously known formulae. Moreover, our formulae take into account the smooth dependence of norming constants on boundary conditions. We also find some new properties of the remainder terms of asymptotics.

math.SP↗

arXiv2016

On the "movement" of the zeros of eigenfunctions of the Sturm-Liouville problem

We study the dependence of the zeros of eigenfunctions of Sturm-Liouville problem on the parameters that define the boundary conditions. As a corollary, we obtain Sturm oscillation theorem, which states that the $n$-th eigenfunction has $n$ zeros.

math.SP↗

arXiv2016

Riesz bases generated by the spectra of Sturm-Liouville problems

Let $\{λ_n^2\}_{n = 0}^\infty$ be the spectra of a Sturm-Liouville problem on $[0,π]$. We investigate the question: Do the systems $\{\cos(λ_n x)\}_{n= 0}^\infty$ or $\{\sin(λ_n x)\}_{n = 0}^\infty$ form Riesz bases in ${L^2}[0,π]$? The answer is almost always positive.

math.SP↗