An \(L^ p\) theory for Schrödinger operators with nonnegative potentials. (English) Zbl 0556.35032

Okazawa, Noboru

J. Math. Soc. Japan 36, 675-688 (1984).

The author studies Schrödinger operators with nonnegative potentials \(V\in L^ P_{loc}({\mathbb{R}}^ m)\). His main purpose is to give sufficient conditions for the m-accretivity of the considered operators. Under further assumptions on the potential he gives regularity results for the solutions of the corresponding Schrödinger equation and a compactness result for the resolvent.

Reviewer: N.Jacob

MSC:

35J10	Schrödinger operator, Schrödinger equation
35Q99	Partial differential equations of mathematical physics and other areas of application
47B44	Linear accretive operators, dissipative operators, etc.
81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords:

Schrödinger operators; nonnegative potentials; m-accretivity; regularity; compactness result; resolvent