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Zero energy asymptotics of the resolvent for a class of slowly decaying potentials

✍ Scribed by S. Fournais; E. Skibsted

Book ID
105874658
Publisher
Springer-Verlag
Year
2004
Tongue
French
Weight
317 KB
Volume
248
Category
Article
ISSN
0025-5874

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✍ Michael Christ; Alexander Kiselev πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 192 KB

We prove the WKB asymptotic behavior of solutions of the differential equation &d 2 uΓ‚dx 2 +V(x) u=Eu for a.e. E>A where V=V 1 +V 2 , V 1 # L p (R), and V 2 is bounded from above with A=lim sup x Γ„ V(x), while V$ 2 (x) # L p (R), 1 p<2. These results imply that Schro dinger operators with such poten