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For the Schrodinger equation $-d^2 u/dx^2 + q(x)u = lambda u$ on a finite $x$-interval, there is defined an asymmetry function $a(lambda;q)$, which is entire of order $1/2$ and type $1$ in $lambda$. Our main result identifies the classes of square-integrable potentials $q(x)$ that possess a common asymmetry function. For any given $a(lambda)$, there is one potential for each Dirichlet spectral sequence.
We consider the Schrodinger operator on $[0,1]$ with potential in $L^1$. We prove that two potentials already known on $[a,1]$ ($ain(0,{1/2}]$) and having their difference in $L^p$ are equal if the number of their common eigenvalues is sufficiently l
We give sufficient conditions for the presence of the absolutely continuous spectrum of a Schrodinger operator on a regular rooted tree without loops (also called regular Bethe lattice or Cayley tree).
We consider the self-adjoint Schrodinger operator in $L^2(mathbb{R}^d)$, $dgeq 2$, with a $delta$-potential supported on a hyperplane $Sigmasubseteqmathbb{R}^d$ of strength $alpha=alpha_0+alpha_1$, where $alpha_0inmathbb{R}$ is a constant and $alpha_
Let $H_0 = -Delta + V_0(x)$ be a Schroedinger operator on $L_2(mathbb{R}^ u),$ $ u=1,2,$ or 3, where $V_0(x)$ is a bounded measurable real-valued function on $mathbb{R}^ u.$ Let $V$ be an operator of multiplication by a bounded integrable real-valued
This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $pi$, we prove that the asymptotics of Steklov eigenvalues obtained in arXiv:1908.06455 determines, in a construc