@article{ZNSL_2020_493_a15,
author = {M. A. Lyalinov},
title = {Eigenfunctions of negative spectrum for the {Schr\"odinger} operator in a halfplane having singular potential on a ray and with {Neumann} boundary condition},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {232--258},
year = {2020},
volume = {493},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a15/}
}
TY - JOUR AU - M. A. Lyalinov TI - Eigenfunctions of negative spectrum for the Schrödinger operator in a halfplane having singular potential on a ray and with Neumann boundary condition JO - Zapiski Nauchnykh Seminarov POMI PY - 2020 SP - 232 EP - 258 VL - 493 UR - http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a15/ LA - ru ID - ZNSL_2020_493_a15 ER -
%0 Journal Article %A M. A. Lyalinov %T Eigenfunctions of negative spectrum for the Schrödinger operator in a halfplane having singular potential on a ray and with Neumann boundary condition %J Zapiski Nauchnykh Seminarov POMI %D 2020 %P 232-258 %V 493 %U http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a15/ %G ru %F ZNSL_2020_493_a15
M. A. Lyalinov. Eigenfunctions of negative spectrum for the Schrödinger operator in a halfplane having singular potential on a ray and with Neumann boundary condition. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 232-258. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a15/
[1] M. A. Lyalinov, “Functional difference equations and eigenfunctions of a Schrödinger operator with $\delta^\prime-$interaction on a circular conical surface”, Proc. Royal Soc. A, 476 (2020), 20200179 | DOI | MR
[2] M. Sh .Birman, M. Z. Solomjak, Spectral theory of selfadjoint operators in Hilbert spaces, Dordrecht, Holland, 1987 | MR
[3] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin, 1995 | MR | Zbl
[4] P. Exner, “Leaky quantum graphs: a review”, Analysis on graphs and its applications, Proc. Sympos. Pure Math., 77, Amer. Math. Soc., Providence, RI, 2008, 523–565 | DOI | MR
[5] B. Behrndt, P. Exner, V. Lotoreichik, “Schrödinger operators with $\delta$- and $\delta'$-interactions on Lipschitz surfaces and chromatic numbers of associated partitions”, Reviews Math. Phys., 26:08 (2014), 1450015–1450058 | DOI | MR
[6] M. Khalile, K. Pankrashkin, “Eigenvalues of Robin Laplacians in infinite sectors”, Math. Nachrichten, 2018, 928–965 | DOI | MR | Zbl
[7] V. M. Babich, “A class of topographical waveguides”, St. Petersburg Math. J., 22 (2011), 73–79 | DOI | MR | Zbl
[8] M. A. Lyalinov, “Kommentarii o sobstvennykh funktsiyakh i sobstvennykh chislakh operatora Laplasa v ugle s kraevymi usloviyami Robena”, Zapis. nauchn. semin. POMI RAN, 483, 2019, 116–127
[9] F. Ursell, “Waves on a sloping beach”, Proc. Royal Soc. London A, 214 (1952), 79–97 | MR | Zbl
[10] N. Kuznetsov, V. Maz'ya, B. Vainberg, Linear Water Waves, Cambridge Univ. Press, Cambridge, 2002 | MR | Zbl
[11] M. Roseau, “Short waves parallel to the shore over a sloping beach”, Comm. Pure Appl. Math., 11 (1958), 433–493 | DOI | MR | Zbl
[12] A. I. Komech, A. E. Merzon, P. N. Zhevandrov, “On the completeness of Ursell's trapping modes”, Russian J. Math. Phys., 1997, no. 4, 457–486 | MR
[13] M. A. Lyalinov, N. Y. Zhu, Scattering of Waves by Wedges and Cones with Impedance Boundary Conditions, Mario Boella Series on Electromagnetism in Information Communication, SciTech–IET, Edison, NJ, 2012
[14] G. D. Maliuzhinets [Malyuzhinets], “Excitation, reflection and emission of surface waves from a wedge with given face impedances”, Soviet Physics: Doklady, 3:4 (1958), 752–755
[15] V. M. Babich, M.A. Lyalinov, V. E. Grikurov, Diffraction Theory. The Sommerfeld-Malyuzhinets Technique, Alpha Science Ser. Wave Phenom., Alpha Science, Oxford, 2008
[16] M. V. Fedoryuk, Asimptotika: integraly i ryady, Nauka, M., 1987 | MR
[17] V. M. Babich, D. B. Dement'ev, B. A. Samokish, V. P. Smyshlyaev, “On evaluation of the diffraction coefficients for arbitrary “Nonsingular” directions of a smooth convex cone”, SIAM J. Appl. Math., 60:2 (2000), 536–573 | DOI | MR | Zbl
[18] I. S. Gradstein, I. M. Ryzhik, Tables of integrals, series and products, 4th ed., Academic Press, Orlando, 1980 | MR
[19] A. A. Fedotov, F. Sandomirskiy, “An exact renormalization formula for the Maryland model”, Commun. Math. Phys., 334 (2015), 1083–1099 | DOI | MR | Zbl
[20] Bernard JML, Méthode analytique et transformées fonctionnelles pour la diffraction d'ondes par une singularité conique: équation intégrale de noyau non oscillant pour le cas d'impédance constante, rapport CEA-R-5764, Dist-Saclay, 1997; erratum in J. Phys. A, 32, L45; an extended version in Bernard JML, Advanced Theory of Diffraction by a Semi-infinite Impedance Cone, Alpha Science Ser. Wave Phenom, Alpha Science, Oxford, UK, 2014
[21] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford Press, 1937 | MR