Quadratic forms for singular perturbations of the Laplacian. (English) Zbl 0735.35048

Teta, Alessandro

Publ. Res. Inst. Math. Sci. 26, No. 5, 803-817 (1990).

The negative Laplacian is defined in \(L_ 2(\mathbb{R}^ 3)\) and singular perturbations of it, ported by points, regular curves and regular surfaces, are considered. The aim is to develop an approach, based on the theory of quadratic forms, for a description of Schrödinger operators in \(L_ 2(\mathbb{R}^ 3)\) with interactions supported by particular sets of Lebesgue measure zero in \(\mathbb{R}^ 3\). The appropriate quadratic forms are constructed and a complete characterisation of the domain, and the action of associated operators is given together with an explicit construction of the resolvent.

Reviewer: G.F.Roach (Glasgow)

MSC:

35J10	Schrödinger operator, Schrödinger equation
35B25	Singular perturbations in context of PDEs
35P05	General topics in linear spectral theory for PDEs

Keywords:

delta-function potentials

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