Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2021_33_2_a11,
author = {A. A. Fedotov},
title = {The complex {WKB} method for a system of two linear difference equations},
journal = {Algebra i analiz},
pages = {298--326},
publisher = {mathdoc},
volume = {33},
number = {2},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AA_2021_33_2_a11/}
}
A. A. Fedotov. The complex WKB method for a system of two linear difference equations. Algebra i analiz, Tome 33 (2021) no. 2, pp. 298-326. http://geodesic.mathdoc.fr/item/AA_2021_33_2_a11/
[1] Wilkinson M., “An exact renormalization group for Bloch electrons in a magnetic field”, J. Phys. A, 20:13 (1987), 4337–4354 | DOI | MR
[2] Helffer B., Sjöstrand J., “Analyse semi-classique pour l'équation de Harper (avec application à l'équationde Schrödinger avec champ magnétique)”, Mém. Soc. Math. France (N.S.), 34 (1988), 1–113 | MR
[3] Babich V., Lyalinov M., Grikurov V., Diffraction theory: The Sommerfeld–Malyuzhinets technique, Alpha Sci., Oxford, 2008
[4] Lyalinov M. A., Zhu N. Y., “A solution procedure for second-order difference equations and its application to electromagnetic-wave diffraction in a wedge-shaped region”, Proc. A, 459:240 (2003), 3159–3180 | MR | Zbl
[5] Buslaev V., Fedotov A., “The monodromization and Harper equation” (1993–1994), Séminaire sur les Équations aux Dérivées Partielles, XXI, École Polytech., Palaiseau, 1994, 1–23 | MR
[6] Fedotov A. F., “Metod monodromizatsii v teorii pochti-periodicheskikh uravnenii”, Algebra i analiz, 25:2 (2013), 203–235
[7] Maslov V. P., Fedoryuk M. V., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR
[8] Dobrokhotov S. Yu., Tsvetkova A. V., “O lagranzhevykh mnogoobraziyakh, svyazannykh s asimptotikoi polinomov Ermita”, Mat. zametki, 104:6 (2018), 835–850 | Zbl
[9] Fedotov A., Klopp F., “The complex WKB method for difference equations and Airy functions”, SIAM J. Math. Anal., 51:6 (2019), 4413–4447 | DOI | MR | Zbl
[10] Fedotov A., Klopp F., “WKB asymptotics of meromorphic solutions to difference equations”, Appl. Analysis, 2019, 17 pp., arXiv: 1903.02224 | DOI
[11] Fedotov A., Shchetka E., “Difference equations in the complex plane: quasiclassical asymptotics and Berry phase”, Appl. Analysis, 2020, 23 pp., arXiv: 1910.09445 | DOI
[12] Fedoryuk M. V., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenenii, Nauka, M., 1983
[13] Sibuya Y., Global theory of a second order linear ordinary differential equation with a polynomial coefficient, North-Holland Math. Stud., 18, North-Holland Publ. Co., Inc., New York, 1975 | MR | Zbl
[14] Wasow W., Asymptotic expansions for ordinary differential equations, Dover Publ., New York, 1987 | MR | Zbl
[15] Buslaev V. S., Fedotov A. A., “Kompleksnyi metod VKB dlya uravneniya Kharpera”, Algebra i analiz, 6:3 (1994), 59–83
[16] Fedotov A. A., Schetka E. V., “Kompleksnyi metod VKB dlya raznostnykh uravnenii v ogranichennykh oblastyakh”, Zap. nauch. semin. POMI, 438, 2015, 236–254
[17] Fedotov A. A., Schetka E. V., “Kompleksnyi metod VKB dlya raznostnogo uravneniya Shredingera, potentsial kotorogo — trigonometricheskii polinom”, Algebra i analiz, 29:2 (2017), 193–219
[18] Pancharatnam S., “Generalized theory of interference, and its applications”, Proc. Indian Acad. Sci. Sect. A, 44 (1956), 247–262 | DOI | MR
[19] Babich V. M., Rusakova N. Ya., “O rasprostranenii voln Releya po poverkhnosti neodnorodnogo uprugogo tela proizvolnoi formy”, Zh. vychisl. mat. i mat. fiz., 2 (1962), 652–665 | Zbl
[20] Berry M., “Quantal phase factors accompanying adiabatic changes”, Proc. Roy. Soc. London Ser. A, 392:1802 (1984), 45–57 | MR | Zbl
[21] Buslaev V. S., Fedotov A. A., “Blokhovskie resheniya dlya raznostnykh uravnenii”, Algebra i analiz, 7 (1995), 74–122
[22] Fedotov A., Klopp F., “Geometric tools of the adiabatic complex WKB method”, Asymptot. Anal., 39:3-4 (2004), 309–357 | MR | Zbl