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Karpeshina, Y.,Lee, Y. R.,Shterenberg, R.,Stolz, G. n. Springer Science + Business Media 2017 Communications in mathematical physics Vol.354 No.1
<P>We prove the existence of ballistic transport for the Schrodinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity assumptions on the potential which have been used in prior work to establish the existence of an absolutely continuous component and other spectral properties. The latter include detailed information on the structure of generalized eigenvalues and eigenfunctions. These allow one to establish the crucial ballistic lower bound through integration by parts on an appropriate extension of a Cantor set in momentum space, as well as through stationary phase arguments.</P>
Karpeshina, Yulia,Lee, Young-Ran Taylor Francis 2008 Communications in partial differential equations Vol.33 No.9
<P> We consider a polyharmonic operator H = (-&Dgr;)l + V(x) in dimension two with l ≥ 6, l being an integer, and a limit-periodic potential V(x). We prove that the spectrum contains a semiaxis of absolutely continuous spectrum.</P>
POLYHARMONIC OPERATORS WITH LIMIT-PERIODIC POTENTIAL
Yulia Karpeshina,Young-Ran Lee 한국산업응용수학회 2007 한국산업응용수학회 학술대회 논문집 Vol.3 No.2
We give a brief survey on spectral properties of polyharmonic operators H=(-△)<SUP>l</SUP>+V(x), l ∈ ?, with a limit-periodic potential V(x)