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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 1, Pages 49–57
DOI: https://doi.org/10.4213/tmf6298 (Mi tmf6298) 		 
This article is cited in 3 scientific papers (total in 3 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
Full-text PDF (384 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf6298
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.
Received: 13.12.2007
Revised: 22.03.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 1, Pages 40–47
DOI: https://doi.org/10.1007/s11232-009-0003-9
Bibliographic databases:
Language: Russian
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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  • https://doi.org/10.4213/tmf6298
  • https://www.mathnet.ru/eng/tmf/v158/i1/p49
    • This publication is cited in the following 3 articles:
    1. Igor Popov, “Magnetic Schrödinger operator on the flat Möbius strip”, Banach J. Math. Anal., 18:3 (2024)  crossref
    2. 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
    3. Eremin D.A., Ivanov D.A., Popov I.Yu., “Regular potential approximation for δ-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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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