Essential spectrum, quasi-orbits and compactifications: application to the Heisenberg group. (English) Zbl 1449.47028
Let \(H\) be the Heisenberg group. Using the natural bijection between \(H\) and \(\mathbb{R}^{3}\), there is introduced a compactification \(\bar{H}\) of \(H\) induced by the spherical compactification of \(\mathbb{R}^{3}\). Let \(T=-\Delta + V\) be the Schrödinger-type operator on \(L^{2}(H)\), where \(V\) is a continuous function on \(\bar{H}\). The main result of the paper gives a representation of the essential spectrum of \(T\) as the union of spectra of some simpler operators. There are also obtained some similar results.
Reviewer: Vladimir S. Pilidi (Rostov-na-Donu)
MSC:
47A53 | (Semi-) Fredholm operators; index theories |
47L65 | Crossed product algebras (analytic crossed products) |
22D25 | \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations |
35J10 | Schrödinger operator, Schrödinger equation |