2007年10月

# Local resolvent estimates for N-body Stark Hamiltonians

LETTERS IN MATHEMATICAL PHYSICS

82
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8

DOI
10.1007/s11005-007-0196-5

SPRINGER

For an N-body Stark Hamiltonian H =- Delta/2-| E| z+ V, the resolvent estimate parallel to &lt; x &gt;(-sigma' -1/4) (H -zeta)(-1) &lt; x &gt;(-sigma'- 1/4) parallel to(B)(L-2) &lt;= C holds uniformly in zeta epsilon C with Re zeta epsilon I and Im zeta not equal 0, where sigma'&gt;0, and I subset of R is a compact interval. This estimate is well known as the limiting absorption principle. In this paper, we report that by introducing the localization q0( x) = root 1- z &lt; x &gt; in the configuration space, a refined resolvent estimate parallel to &lt; x &gt;(-1 4) q0(x)( H -zeta)(-1) q0(x) &lt; x &gt;(-1/4) parallel to B( L-2) &lt;= C holds uniformly in zeta epsilon C with Re zeta epsilon I and Im zeta not equal 0.

Web of Science ® 被引用回数 : 1

リンク情報
DOI
https://doi.org/10.1007/s11005-007-0196-5
Web of Science