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Schrödinger Operators with Sparse Potentials: Asymptotics of the Fourier Transform¶of the Spectral Measure

✍ Scribed by Denis Krutikov; Christian Remling

Publisher
Springer
Year
2001
Tongue
English
Weight
174 KB
Volume
223
Category
Article
ISSN
0010-3616

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✍ Shmuel Agmon; Jaime Cruz-Sampedro; Ira Herbst 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 206 KB

We investigate the Schro dinger operator H=&2+V acting in L 2 (R n ), n 2, for potentials V that satisfy : x V(x)=O(|x| &|:| ) as |x| Ä . By introducing coordinates on R n closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.