The spectrum of a Schrödinger operator in \(L_ p({\mathbb{R}}^{\nu})\) is p-independent. (English) Zbl 0593.35033
Let \(H_ p=-()\Delta +V\) denote a Schrödinger operator, acting in \(L_ p({\mathbb{R}}^ n)\), \(1\leq p\leq \infty\). It is shown that \(\sigma (H_ p)=\sigma (H_ 2)\) for all \(p\in [1,\infty]\), for a rather general class of potentials V.
Reviewer: Michael Sever (Jerusalem)
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35P99 | Spectral theory and eigenvalue problems for partial differential equations |
References:
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