arXiv math/04081832004-08-13math.SPmath-phmath.MP

Several complex variables and the distribution of resonances in potential scattering

T. Christiansen

备注：: 18 pages
DOI：: 10.1007/s00220-005-1381-y

英文摘要：

We study resonances associated to Schrödinger operators with compactly supported potentials on ${\mathbb R}^d$, $d\geq3$, odd. We consider compactly supported potentials depending holomorphically on a complex parameter $z$. For certain such families, for all $z$ except those in a pluripolar set, the associated resonance-counting function has order of growth $d$. Our proofs use some results from several complex variables.

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