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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 large. The result here is to write down explicitly this number in terms of $p$ (and $a$) showing the role of $p$.
We study the direct and inverse scattering problem for the one-dimensional Schrodinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed smoothness and
This is the second in a series of papers on scattering theory for one-dimensional Schrodinger operators with Miura potentials admitting a Riccati representation of the form $q=u+u^2$ for some $uin L^2(R)$. We consider potentials for which there exist
The spectrum of the singular indefinite Sturm-Liouville operator $$A=text{rm sgn}(cdot)bigl(-tfrac{d^2}{dx^2}+qbigr)$$ with a real potential $qin L^1(mathbb R)$ covers the whole real line and, in addition, non-real eigenvalues may appear if the poten
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-in
We consider a Schrodinger operator with complex-valued potentials on the line. The operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half-line. We determi