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تسجيل مستخدم جديدA regularity result for the bound states of $N$-body Schrodinger operators: Blow-ups and Lie manifolds
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We prove regularity estimates for the eigenfunctions of Schrodinger type operators whose potentials have inverse square singularities and uniform radial limits at infinity. In particular, the usual $N$-body operators are covered by our result; in that case, the weight is in terms of the (euclidean) distance to the collision planes. The technique of proof is based on blow-ups and Lie manifolds. More precisely, we first blow-up the spheres at infinity of the collision planes to obtain the Georgescu-Vasy compactification and then we blow-up the collision planes. We carefully investigate how the Lie manifold structure and the associated data (metric, Sobolev spaces, differential operators) change with each blow-up. Our method applies also to higher order operators and matrices of scalar operators.
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