A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds
by
Bernd Ammann, Jérémy Mougel, Victor Nistor
A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds
(.pdf)
Lett. Math. Phys. 113, 26-53 (2023)
Arxiv: https://arxiv.org/abs/2012.13902
DOI: 10.1007/s11005-023-01648-0
©-info: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Journal Mathematical Physics (Springer), and is available online at https://doi.org/10.1007/s11005-023-01648-0
We prove regularity estimates for the eigenfunctions of Schrödinger 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.
- In the published version, page 4, between equation (3) and (4), there are two typos in the phrase starting with "More precisely" and the following phrases. At first the variable A is used in two senses.
Secondly the publisher has added an incorrect dot after the word semilattice. The pdf-file given above is corrected.
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The Paper was written on 28.12.2020
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