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Schrödinger operators on regular metric trees with long range potentials: Weak coupling behavior |
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| Authors: | Tomas Ekholm,Hynek Kova?í k |
| Affiliation: | a Department of Mathematics, Lund University, S-221 00 Lund, Sweden b Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden c Dipartimento di Matematica, Politecnico di Torino, I-101 29 Torino, Italy |
| Abstract: | Consider a regular d-dimensional metric tree Γ with root o. Define the Schrödinger operator −Δ−V, where V is a non-negative, symmetric potential, on Γ, with Neumann boundary conditions at o. Provided that V decays like |x|−γ at infinity, where 1<γ?d?2, γ≠2, we will determine the weak coupling behavior of the bottom of the spectrum of −Δ−V. In other words, we will describe the asymptotic behavior of infσ(−Δ−αV) as α→0+. |
| Keywords: | Schrö dinger operators Metric trees Fourier-Bessel transformation Weak coupling |
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