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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 100, Number 3, Pages 354–366 (Mi tmf1654)  

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

The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators

A. A. Kiseleva, B. S. Pavlovb

a Saint-Petersburg State University
b V. A. Fock Institute of Physics, Saint-Petersburg State University
References:
Abstract: The model Neuman Laplacian in the system of two resonators, connected through a thin channel, is studied. The first terms of the asymptotic expansions of eigenvalues and eigenfunctions by small linking parameter are obtained. An explicit expression for resolvent is derived. The model problem is compared to a real one.
Received: 05.04.1993
English version:
Theoretical and Mathematical Physics, 1994, Volume 100, Issue 3, Pages 1065–1074
DOI: https://doi.org/10.1007/BF01018571
Bibliographic databases:
Language: Russian
Citation: A. A. Kiselev, B. S. Pavlov, “The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators”, TMF, 100:3 (1994), 354–366; Theoret. and Math. Phys., 100:3 (1994), 1065–1074
Citation in format AMSBIB
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\by A.~A.~Kiselev, B.~S.~Pavlov
\paper The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators
\jour TMF
\yr 1994
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\issue 3
\pages 354--366
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\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 100
\issue 3
\pages 1065--1074
\crossref{https://doi.org/10.1007/BF01018571}
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Linking options:
  • https://www.mathnet.ru/eng/tmf1654
  • https://www.mathnet.ru/eng/tmf/v100/i3/p354
  • This publication is cited in the following 11 articles:
    1. Dozyslav B. Kuryliak, Oleksiy M. Sharabura, “Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity”, Applied Sciences, 13:14 (2023), 8517  crossref
    2. Vorobiev A.M., “Resonance Asymptotics For Quantum Waveguides With Semitransparent Multi-Perforated Wall”, Nanosyst.-Phys. Chem. Math., 12:4 (2021), 462–471  crossref  isi
    3. Vorobiev A.M. Trifanova E.S. Popov I.Y., “Resonance Asymptotics For a Pair Quantum Waveguides With Common Semitransparent Perforated Wall”, Nanosyst.-Phys. Chem. Math., 11:6 (2020), 619–627  crossref  isi
    4. Vorobiev A.M. Bagmutov A.S. Popov I A., “On Formal Asymptotic Expansion of Resonance For Quantum Waveguide With Perforated Semitransparent Barrier”, Nanosyst.-Phys. Chem. Math., 10:4 (2019), 415–419  crossref  isi
    5. Dozyslav B. Kuryliak, Zinoviy Theodorovych Nazarchuk, Oksana B. Trishchuk, “AXIALLY-SYMMETRIC TM-WAVES DIFFRACTION BY SPHERE-CONICAL CAVITY”, PIER B, 73 (2017), 1  crossref
    6. R. R. Gadyl'shin, “On the eigenvalues of a “dumb-bell with a thin handle””, Izv. Math., 69:2 (2005), 265–329  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Pavlov, BS, “Possible construction of a quantum multiplexer”, Europhysics Letters, 52:2 (2000), 196  crossref  adsnasa  isi
    8. V.A. Geyler, I.Yu. Popov, S.L. Popova, “Transmission coefficient for ballistic transport through quantum resonator”, Reports on Mathematical Physics, 40:3 (1997), 531  crossref
    9. Alexander Kiselev, “Some Examples in One-Dimensional “Geometric” Scattering on Manifolds”, Journal of Mathematical Analysis and Applications, 212:1 (1997), 263  crossref
    10. R. R. Gadyl'shin, “On scattering by cylinder with narrow slit and with shell of finite depth”, Theoret. and Math. Phys., 106:1 (1996), 19–34  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. V. A. Geiler, I. Yu. Popov, “Ballistic transport in nanostructures: explicitly solvable models”, Theoret. and Math. Phys., 107:1 (1996), 427–434  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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