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Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in $\mathbb R^4$

Yu. G. Shondin

Nizhny Novgorod State Pedagogical University

Abstract: Perturbations supported by curves with angle points are studied for the Laplacian in $\mathbb R^4$ within the framework of the extension theory. Classes of the self-adjoint extensions that are local, semibounded and generate a positivity preserving semigroup are distinguished. Their connection with the local Dirichlet forms is obtained.

Received: 17.05.1995

DOI: 10.4213/tmf1106

 English version: Theoretical and Mathematical Physics, 1996, 106:2, 151–166

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