Zobrazeno 1 - 10
of 1 241
pro vyhledávání: '"34L40"'
Autor:
Remling, Christian, Zeng, Jie
We study canonical systems that are reflectionless on an open set. In this situation, the two half line $m$ functions are holomorphic continuations of each other and may thus be combined into a single holomorphic function. This idea was explored in [
Externí odkaz:
http://arxiv.org/abs/2410.20218
We characterise regions in the complex plane that contain all non-embedded eigenvalues of a perturbed periodic Dirac operator on the real line with real-valued periodic potential and a generally non-symmetric matrix-valued perturbation V . We show th
Externí odkaz:
http://arxiv.org/abs/2410.12467
Autor:
Bondarenko, Natalia P.
In this paper, we prove the uniform stability of the Hochstadt-Lieberman problem, which consists in the recovery of the Sturm-Liouville potential on a half-interval from the spectrum and the known potential on the other half-interval. For this purpos
Externí odkaz:
http://arxiv.org/abs/2410.10326
Autor:
Schino, Jacopo, Smyrnelis, Panayotis
Given $m \in \mathbb{N} \setminus \{0\}$ and $\rho > 0$, we find solutions $(\lambda,u)$ to the problem \begin{equation*} \begin{cases} \bigl(-\frac{\mathrm{d}^2}{\mathrm{d} x^2}\bigr)^m u + \lambda G'(u) = F'(u)\\ \int_{\mathbb{R}} K(u) \, \mathrm{d
Externí odkaz:
http://arxiv.org/abs/2410.03318
We derive necessary and sufficient conditions for universality limits for orthogonal polynomials on the real line and related systems. One of our results is that the Christoffel-Darboux kernel has sine kernel asymptotics at a point $\xi$, with regula
Externí odkaz:
http://arxiv.org/abs/2409.18045
Autor:
Bondarenko, Natalia P.
In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm-Liouville problem that consists in the recovery of the potential and the parameters of the bounda
Externí odkaz:
http://arxiv.org/abs/2409.16175
Autor:
Badanin, Andrey
We consider a third order operator under the three-point Dirichlet condition. Its spectrum is the so-called auxiliary spectrum for the good Boussinesq equation, as well as the Dirichlet spectrum for the Schr\"odinger operator on the unit interval is
Externí odkaz:
http://arxiv.org/abs/2409.10988
Autor:
Papanicolaou, Vassilis G.
Let $H = -d^2/dx^2 + q(x)$, $x \in \mathbb{R}$, where $q(x)$ is a periodic potential, and suppose that the spectrum $\sigma(H)$ of $H$ is the positive semi-axis $[0, \infty)$. In the case where $q(x)$ is real-valued (and locally square-integrable) a
Externí odkaz:
http://arxiv.org/abs/2409.10266
Autor:
Gubkin, Pavel
We prove that mean decay of the coefficient of Krein system is equivalent to the mean decay of the Fourier transform of its Szeg\H{o} function.
Externí odkaz:
http://arxiv.org/abs/2409.08614
In this work we analyze the spectral $\zeta$-function associated with the self-adjoint extensions, $T_{A,B}$, of quasi-regular Sturm--Liouville operators that are bounded from below. By utilizing the Green's function formalism, we find the characteri
Externí odkaz:
http://arxiv.org/abs/2409.06922