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

This article is cited in 8 scientific papers (total in 8 papers)

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:

Received: 17.05.1995

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
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\by Yu.~G.~Shondin
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\pages 179--199
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\jour Theoret. and Math. Phys.
\yr 1996
\vol 106
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\pages 151--166
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Geyler V.A., Pankrashkin K.V., “On fractal structure of the spectrum for periodic point perturbations of the Schrodinger operator with a uniform magnetic field”, Mathematical Results in Quantum Mechanics, Operator Theory : Advances and Applications, 108, 1999, 259–265  mathscinet  zmath  adsnasa  isi
    2. Albeverio, S, “The band structure of the general periodic Schrodinger operator with point interactions”, Communications in Mathematical Physics, 210:1 (2000), 29  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    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  mathscinet  zmath  isi
    4. K. V. Pankrashin, “Locality of Quadratic Forms for Point Perturbations of Schrödinger Operators”, Math. Notes, 70:3 (2001), 384–391  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Geyler, VA, “Transport in the two-terminal Aharonov-Bohm ring”, Technical Physics, 48:6 (2003), 661  crossref  adsnasa  isi  scopus  scopus
    6. Geyler, VA, “Zero modes in a system of Aharonov-Bohm fluxes”, Reviews in Mathematical Physics, 16:7 (2004), 851  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Brasche, JF, “Interactions along Brownian paths in R-d, d <= 5”, Journal of Physics A-Mathematical and General, 38:22 (2005), 4755  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    8. Kurasov, P, “Finite speed of propagation and local boundary conditions for wave equations with point interactions”, Proceedings of the American Mathematical Society, 133:10 (2005), 3071  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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