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TMF, 2009, Volume 158, Number 1, Pages 49–57 (Mi tmf6298)  

This article is cited in 2 scientific papers (total in 2 papers)

Approximation of a point perturbation on a Riemannian manifold

V. A. Geiler, D. A. Ivanova, I. Yu. Popovb

a Mordovian State University
b St. Petersburg State University of Information Technologies, Mechanics and Optics

Abstract: We show that the Hamiltonian of point interaction on a Riemannian manifold with bounded geometry can be obtained as a limit (in the sense of uniform resolvent convergence) of a sequence of scaling Hamiltonians with short-range interaction.

Keywords: Riemannian manifold, point interaction, approximation

DOI: https://doi.org/10.4213/tmf6298

Full text: PDF file (384 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2009, 158:1, 40–47

Bibliographic databases:

Received: 13.12.2007
Revised: 22.03.2008

Citation: V. A. Geiler, D. A. Ivanov, I. Yu. Popov, “Approximation of a point perturbation on a Riemannian manifold”, TMF, 158:1 (2009), 49–57; Theoret. and Math. Phys., 158:1 (2009), 40–47

Citation in format AMSBIB
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\paper Approximation of a~point perturbation on a~Riemannian manifold
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  • http://mi.mathnet.ru/eng/tmf/v158/i1/p49

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Eremin D.A., Ivanov D.A., “Matematicheskaya model lipkogo kvantovogo grafa na sfere: chislennaya approksimatsiya”, Novyi universitet. Ser. Voprosy estestvennykh nauk, 2012, no. 2, 3–5  elib
    2. Eremin D.A., Ivanov D.A., Popov I.Yu., “Regular potential approximation for $\delta$-perturbation supported by curve of the Laplace–Beltrami operator on the sphere”, Z. Anal. ihre. Anwend., 31:2 (2012), 125–137  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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