Nonselfadjoint Schrödinger operators with singular first-order coefficients. (English) Zbl 0555.35025
The operator of the form \(T=(i\nabla +b)^ 2+a\nabla +q\) in \(L^ 2(R^ m)\) with domain \(C_ 0^{\infty}(R^ m)\) is considered. If a, b are real valued vector functions such that \(b\in L^ 4_{loc}\), \(div b\in L^ 2_{loc},\) \((1+| x|)^{-1}a\in L^ 4+L^{\infty},\) \(div a\in L^{\infty}\) and \(q\in L^ 2_{loc}\), Re \(q\geq 0\), then the essential-m-accretivity of the operator T is proved.
Reviewer: M.A.Perelmuter
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 47H06 | Nonlinear accretive operators, dissipative operators, etc. |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
Keywords:
nonselfadjoint Schrödinger operators; singular first-order coefficients; essential-m-accretivityReferences:
| [1] | DOI: 10.1016/0022-1236(79)90079-X · Zbl 0413.47037 · doi:10.1016/0022-1236(79)90079-X |
| [2] | DOI: 10.1007/BF01258900 · Zbl 0468.35038 · doi:10.1007/BF01258900 |
| [3] | Wong-Dzung, Proc. Roy. Soc. Edinburgh Sect. A 95 pp 95– (1983) · Zbl 0548.35051 · doi:10.1017/S030821050001581X |
| [4] | Flanders, Differential Forms (1963) |
| [5] | DOI: 10.1007/BF02760233 · Zbl 0246.35025 · doi:10.1007/BF02760233 |
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