Yu. G. Shondin, “About semiboundness of $\delta$-perturbations of the Laplacian supported by curves with angle points”, TMF, 105:1 (1995), 3–17; Theoret. and Math. Phys., 105:1 (1995), 1189

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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 105, Number 1, Pages 3–17 (Mi tmf1358)

This article is cited in 11 scientific papers (total in 11 papers)

About semiboundness of $\delta$-perturbations of the Laplacian supported by curves with angle points

Yu. G. Shondin

Nizhny Novgorod State Pedagogical University

Full-text PDF (1555 kB) Citations (11)

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Abstract: Еlementary self-adjoint perturbations of the Laplacian supported by curves with singular angle points are studied in $\mathbb R^3$ and $\mathbb R^4$. The perturbations are shown to be semibounded in $\mathbb R^3$ and unsemibounded in $\mathbb R^4$. In the last case semiboundness may take place in subspaces of a given symmetry as it is shown in simple example.

Received: 23.11.1994
Revised: 15.02.1995

English version:
Theoretical and Mathematical Physics, 1995, Volume 105, Issue 1, Pages 1189–1200
DOI: https://doi.org/10.1007/BF02067488

Bibliographic databases:

Language: Russian

Citation: Yu. G. Shondin, “About semiboundness of $\delta$-perturbations of the Laplacian supported by curves with angle points”, TMF, 105:1 (1995), 3–17; Theoret. and Math. Phys., 105:1 (1995), 1189–1200

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

\yr 1995

\vol 105

\issue 1

\pages 1189--1200

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Linking options:

https://www.mathnet.ru/eng/tmf1358

https://www.mathnet.ru/eng/tmf/v105/i1/p3

This publication is cited in the following 11 articles:

Gianfausto Dell'Antonio, Springer Proceedings in Mathematics & Statistics, 377, Quantum and Stochastic Mathematical Physics, 2023, 107
Behrndt J., Frank R.L., Kuehn Ch., Lotoreichik V., Rohleder J., “Spectral Theory for Schrödinger Operators with
$$\varvec{\delta }$$
-Interactions Supported on Curves in
$$\varvec{\mathbb {R}^3}$$
R 3”, Ann. Henri Poincare, 18:4 (2017), 1305–1347
S. V. Talalov, “Ob effekte perenosa massy vdol kosmicheskoi struny”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(31) (2013), 259–266
E. A. Vedutenko, S. V. Talalov, “Model rasseyaniya neitralnoi kvantovoi chastitsy na nestatsionarnoi krivoi”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 3(104), 85–89
Talalov S.V., “About the Mechanism of Matter Transfer Along the Cosmic String”, Mod. Phys. Lett. A, 27:8 (2012), 1250048
Brasche, JF, “Interactions along Brownian paths in R-d, d <= 5”, Journal of Physics A-Mathematical and General, 38:22 (2005), 4755
Pavel Exner, Kazushi Yoshitomi, “Asymptotics of eigenvalues of the Schrödinger operator with a strong δ-interaction on a loop”, Journal of Geometry and Physics, 41:4 (2002), 344
Andrea Posilicano, Operator Methods in Ordinary and Partial Differential Equations, 2002, 333
Andrea Posilicano, “A Krein-like Formula for Singular Perturbations of Self-Adjoint Operators and Applications”, Journal of Functional Analysis, 183:1 (2001), 109
I. Yu. Popov, D. A. Zubok, “Two physical applications of the Laplace operator perturbed on a null set”, Theoret. and Math. Phys., 119:2 (1999), 629–639
Yu. G. Shondin, “Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in $\mathbb R^4$”, Theoret. and Math. Phys., 106:2 (1996), 151–166

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

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References:	48
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