Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Remling, Christian"'
Autor:
Remling, Christian
I prove a sharp bound on reflectionless Dirac operators.
Externí odkaz:
http://arxiv.org/abs/2412.01599
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
Autor:
Forester, Max, Remling, Christian
We study the topological properties of spaces of reflectionless canonical systems. In this analysis, a key role is played by a natural action of the group $\operatorname{PSL}(2,\mathbb R)$ on these spaces.
Externí odkaz:
http://arxiv.org/abs/2409.04862
Autor:
Remling, Christian, Scarbrough, Kyle
We study the minimum of the essential spectrum of canonical systems $Ju'=-zHu$. Our results can be described as a generalized and more quantitative version of the characterization of systems with purely discrete spectrum, which was recently obtained
Externí odkaz:
http://arxiv.org/abs/1908.02266
Autor:
Remling, Christian, Scarbrough, Kyle
Oscillation theory locates the spectrum of a differential equation by counting the zeros of its solutions. We present a version of this theory for canonical systems $Ju'=-zHu$ and then use it to discuss semibounded operators from this point of view.
Externí odkaz:
http://arxiv.org/abs/1811.07067
Autor:
Ong, Darren C., Remling, Christian
The classical hierarchy of Toda flows can be thought of as an action of the (abelian) group of polynomials on Jacobi matrices. We present a generalization of this to the larger groups of $C^2$ and entire functions, and in this second case, we also in
Externí odkaz:
http://arxiv.org/abs/1801.03053
Autor:
Remling, Christian
I present a discussion of the hierarchy of Toda flows that gives center stage to the associated cocycles and the maps they induce on the $m$ functions. In the second part, these ideas are then applied to canonical systems; an important feature of thi
Externí odkaz:
http://arxiv.org/abs/1712.00503
Autor:
Remling, Christian, Scarbrough, Kyle
Publikováno v:
In Journal of Approximation Theory June 2020 254
The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles
We develop the inverse scattering transform for the KdV equation with real singular initial data $q(x)$ of the form $q(x) = r'(x) + r(x)^2$, where $r\in L^2_{\textrm{loc}}$ and $r=0$ on $\mathbb R_+$. As a consequence we show that the solution $q(x,t
Externí odkaz:
http://arxiv.org/abs/1412.2184