Spherical perturbations of Schrodinger equations
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Colleges, School and Institutes
We give conditions on radial nonnegative weights W-1 and W-2 on R-n for which the a priori inequality parallel to(-Delta(S))(1/2)u parallel to(L2(W1) = 3. As a consequence we establish some new estimates for the free Schrodinger propagator e(it=Delta), which may be viewed as certain refinements of the Delta-(super)smoothness estimates of Kato and Yajima. These results, in turn, lead to the well-posedness of the initial value problem for certain time dependent first order spherical perturbations of then >= 3 dimensional Schrodinger equation.
|Number of pages||22|
|Journal||Journal of Fourier Analysis and Applications|
|Publication status||Published - 1 Jun 2006|