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 TMF, 1996, Volume 106, Number 2, Pages 179–199 (Mi tmf1106)

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.

DOI: https://doi.org/10.4213/tmf1106

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

Bibliographic databases:

Citation: Yu. G. Shondin, “Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in $\mathbb R^4$”, TMF, 106:2 (1996), 179–199; Theoret. and Math. Phys., 106:2 (1996), 151–166

Citation in format AMSBIB
\Bibitem{Sho96} \by Yu.~G.~Shondin \paper Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in~$\mathbb R^4$ \jour TMF \yr 1996 \vol 106 \issue 2 \pages 179--199 \mathnet{http://mi.mathnet.ru/tmf1106} \crossref{https://doi.org/10.4213/tmf1106} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1402004} \zmath{https://zbmath.org/?q=an:0890.35037} \transl \jour Theoret. and Math. Phys. \yr 1996 \vol 106 \issue 2 \pages 151--166 \crossref{https://doi.org/10.1007/BF02071070} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996VN51500001} 

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This publication is cited in the following articles:
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2. Albeverio, S, “The band structure of the general periodic Schrodinger operator with point interactions”, Communications in Mathematical Physics, 210:1 (2000), 29
3. Bruning J., Geyler V.A., “The spectrum of periodic point perturbations and the Krein resolvent formula”, Differential Operators and Related Topics, Operator Theory : Advances and Applications, 117, 2000, 71–86
4. K. V. Pankrashin, “Locality of Quadratic Forms for Point Perturbations of Schrödinger Operators”, Math. Notes, 70:3 (2001), 384–391
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