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In the present work we consider in $L^2(\mathbb{R}_+)$ the Schr\"odinger operator $\mathrm{H_{X,\alpha}}=-\mathrm{\frac{d^2}{dx^2}}+\sum_{n=1}^{\infty}\alpha_n\delta(x-x_n)$. We investigate and comple...
It is shown that Schrodinger operators defined from the standard map have positive (mean) Lyapounov exponents for almost all energies.
Abstract: We prove that radial, monotonic, superexponentially decaying potentials in R^n, n greater than or equal to 1 odd, are determined by the resonances of the associated semiclassical Schrodinger...
We observe that some special Itˆo diffusions are related to scattering properties of a Schr¨odinger operator on Rd, d  2. We introduce Feynman-Kac type formulae for these stochastic processes wh...
The purpose of this paper is to give some refined results about the distribution of resonances in potential scattering. We use techniques and results from one and several complex variables, including ...
We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schr¨odinger operators of the form L = − + V , where the nonnegative pot...
New Completely Integrable (2+1)-System is studied. It is based on the so-called L-A-B-triples $L_t=[H,L]-fL$ where L is a 2D Schrodinger Operator. This approach was invented by S.Manakov and B.Dubrovi...
Let Ω be a bounded Lipschitz domain in ,nRn≥3 . Let 0()QQQααω =|− |, where 0Q is a fixed point on Ω∂ . For Schrödinger equation 0 uVu −Δ+ = in Ω , with singular non-neg...

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