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  • D. Krejčiřík (a1), N. Raymond (a2), J. Royer (a3) and P. Siegl (a4) (a5)

This paper is devoted to dimensional reductions via the norm-resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its application on seemingly different partial differential equation problems from various areas of mathematical physics; all are analysed in a unified manner, known results are recovered and new ones established.

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2. Borisov, D. and Krejčiřík, D., The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions. Asymptot. Anal. 76(1) 2012, 4959.
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6. Helffer, B. and Kachmar, A., Eigenvalues for the Robin Laplacian in domains with variable curvature. Trans. Amer. Math. Soc. 369(5) 2017, 32533287.
7. Helffer, B., Kachmar, A. and Raymond, N., Tunneling for the Robin Laplacian in smooth planar domains. Commun. Contemp. Math. 19(1) 2017, 1650030, 38.
8. Jecko, T., On the mathematical treatment of the Born–Oppenheimer approximation. J. Math. Phys. 55(5) 2014, 053504, 26.
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10. Krejčiřík, D. and Raymond, N., Magnetic effects in curved quantum waveguides. Ann. Henri Poincaré 15(10) 2014, 19932024.
11. Krejčiřík, D., Raymond, N. and Tušek, M., The magnetic Laplacian in shrinking tubular neighborhoods of hypersurfaces. J. Geom. Anal. 25(4) 2015, 25462564.
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13. Lampart, J. and Teufel, S., The adiabatic limit of the Laplacian on thin fibre bundles. In Microlocal Methods in Mathematical Physics and Global Analysis (Trends in Mathematics), Birkhäuser/Springer (Basel, 2013), 3336.
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16. Oliveira, C. R. d. and Rossini, A. F., Effective operators for Robin Laplacian in thin two- and three-dimensional curved waveguides. Submitted for publication.
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18. Raymond, N., Bound States of the Magnetic Schrödinger Operator (EMS Tracts 27 ), European Mathematical Society (Zurich, 2017).
19. Wachsmuth, J. and Teufel, S., Effective Hamiltonians for constrained quantum systems. Mem. Amer. Math. Soc. 230(1083) 2014.
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  • ISSN: 0025-5793
  • EISSN: 2041-7942
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