TY - JOUR
T1 - Generalized Fourier Transform for Schrödinger Operators with Potentials of Order Zero
AU - Agmon, Shmuel
AU - Cruz-Sampedro, Jaime
AU - Herbst, Ira
PY - 1999/10/1
Y1 - 1999/10/1
N2 - We investigate the Schrödinger operator H=-Δ+V acting in L2(Rn), n≥2, for potentials V that satisfy ∂αxV(x)=O(x-α) as x→∞. By introducing coordinates on Rn closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.
AB - We investigate the Schrödinger operator H=-Δ+V acting in L2(Rn), n≥2, for potentials V that satisfy ∂αxV(x)=O(x-α) as x→∞. By introducing coordinates on Rn closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.
UR - http://www.scopus.com/inward/record.url?scp=0007543072&partnerID=8YFLogxK
U2 - 10.1006/jfan.1999.3432
DO - 10.1006/jfan.1999.3432
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AN - SCOPUS:0007543072
SN - 0022-1236
VL - 167
SP - 345
EP - 369
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -