arXiv subjects

Tigran Harutyunyan

Publications and source records attributed to Tigran Harutyunyan.

8 recordsLinked to original sources

arXiv2024

Spectral Theory of Dirac Operators

The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in eigenfunctions, uniqueness theorems in inverse problems, constructive solution of inverse problems, description of isospectral operators, and some other questions. This book is aimed at specialists in spectral theory and graduate students of mathematics at universities.

math.SP↗

arXiv2018

Inverse Sturm-Liouville problems with summable potential

We describe the necessary and sufficient conditions for two sequences {μ_n}^\infty_n=0 and {a_n}^\infty_n=0 to be correspondingly the set of eigenvalues and the set of norming constants of a Sturm-Liouville problem with real summable potential q and in advance fixed separated boundary conditions.

math.SP↗

arXiv2017

Gradient of eigenvalues of Dirac operators and its applications

For Dirac operators, which have discrete spectra, the concept of eigenvalues gradient is given and formulae for this gradients are obtained in terms of normalized eigenfunctions. It is shown how the gradient is being used to describe isospectral operators or when finite number of spectral data is changed.

math.CA↗

arXiv2017

Isospectral Dirac operators

We give the description of self-adjoint regular Dirac operators, on $[0, π]$, with the same spectra.

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

Inverse Sturm-Liouville problems with fixed boundary conditions

Necessary and sufficient conditions for two sequences $\{μ_n\}_{n=0}^\infty$ and $\{ a_n\}_{n=0}^\infty$ to be the spectral data for a certain Sturm-Liouville problem are well known. We add two more conditions so that the same two sequences become necessary and sufficient for being the spectral data for a Sturm-Liouville problem with fixed boundary conditions.

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↗