Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MMO_2020_81_2_a0, author = {A. G. Sergeev}, title = {Applications of noncommutative geometry in function theory and mathematical physics}, journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva}, pages = {145--203}, publisher = {mathdoc}, volume = {81}, number = {2}, year = {2020}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MMO_2020_81_2_a0/} }
TY - JOUR AU - A. G. Sergeev TI - Applications of noncommutative geometry in function theory and mathematical physics JO - Trudy Moskovskogo matematičeskogo obŝestva PY - 2020 SP - 145 EP - 203 VL - 81 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MMO_2020_81_2_a0/ LA - ru ID - MMO_2020_81_2_a0 ER -
A. G. Sergeev. Applications of noncommutative geometry in function theory and mathematical physics. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 81 (2020) no. 2, pp. 145-203. http://geodesic.mathdoc.fr/item/MMO_2020_81_2_a0/
[1] L. Alfors, Lektsii po kvazikonformnym otobrazheniyam, Mir, M., 1969
[2] N. Ashkroft, N. Mermin, Fizika tverdogo tela, Mir, M., 1979
[3] F. A. Berezin, M. A. Shubin, Uravnenie Shredingera, MGU, M., 1983
[4] J. Bellisard, A. van Elst, H. Schulz-Baldes, “The noncommutative geometry of the quantum Hall effect”, J. Math. Phys., 35 (1994), 5373–5451 | DOI | MR
[5] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, M., 1986 | MR
[6] R. Bowen, “Hausdorff dimension of quasi-circles”, Publ. Math. IHES, 50 (1979), 259–273 | MR
[7] A. Carey, K. Hannabuss, V. Mathai, P. J. McCan, “Quantum Hall effect on the hyperbolic plane”, Commun. Math. Phys., 190 (1998), 629–673 | DOI | MR | Zbl
[8] A. Connes, Noncommutative geometry, Academic Press, San Diego, 1994 | MR | Zbl
[9] H. M. Farkas, I. Kra, Riemann surfaces, Springer, New York, 1992 | MR | Zbl
[10] J. M. Gracia-Bondía, J. C. Varilly, H. Figueroa, Elements of noncommutative geometry, Birkhauser, Boston, 2001 | MR | Zbl
[11] S. Janson, T. H. Wolff, “Schatten classes and commutators of singular integral operators”, Ark. Mat., 20 (1982), 301–310 | DOI | MR | Zbl
[12] Yu. Kordyukov, V. Mathai, M. Shubin, “Equivalence of spectral projection in semi-classical limit and a vanishing theorem for higher traces in K-theory”, J. Reine Angew. Math., 581 (2005), 193–236 | DOI | MR | Zbl
[13] E. M. Lifshits, L. P. Pitaevskii, Statisticheskaya fizika, v. 2, Nauka, M., 1978 | MR
[14] R. B. Laughlin, “Quantized Hall conductivity in two dimensions”, Phys. Rev., B23 (1981), 5632 | DOI
[15] H. B. Lawson jr., M.-L. Michelsohn, Spin geometry, Princeton University Press, Princeton, New Jersey, 1989 | MR | Zbl
[16] O. Lehto, Univalent functions and Teichmuller spaces, Grad. Texts Math., 109, Springer, New York, 1987 | DOI | MR | Zbl
[17] M. Marcolli, V. Mathai, “Towards the fractional quantum Hall effect: a noncommutative geometry perspective”, Noncommutative Geometry and Number Theory, Aspects Math., E 37, Friedr. Vieweg Verlag, Wiesbaden, 2006, 235–261 | MR
[18] S. Nag, D. Sullivan, “Teichmuller theory and the universal period mapping via quantum calculus and the $H^{1/2}$ space on the circle”, Osaka J. Math., 32 (1995), 1–34 | MR | Zbl
[19] M. A. Naimark, Normirovannye koltsa, Fizmatlit, M., 2010 | MR
[20] V. V. Peller, Operatory Gankelya i ikh prilozheniya, RKhD, Izhevsk, 2005
[21] S. C. Power, Hankel operators on Hilbert space, Research Notes in Math., 64, Pitman, Boston–London–Melbourne, 1982 | MR | Zbl
[22] H. M. Reimann, “Ordinary differential equations and quasiconformal mappings”, Invent. Math., 33 (1976), 247–270 | DOI | MR | Zbl
[23] U. Rudin, Funktsionalnyi analiz, Mir, M., 1975
[24] G. Segal, “Unitary representations of some infinite dimensional groups”, Commun. Math. Phys., 80 (1981), 301–342 | DOI | MR | Zbl
[25] A. G. Sergeev, Lectures on universal Teichmuller space, EMS, Zürich, 2014 | MR | Zbl
[26] A. G. Sergeev, Geometricheskoe kvantovanie prostranstv petel, Sovr. probl. matem., 13, MIAN, M., 2009
[27] A. G. Sergeev, “Kvantovoe ischislenie i idealy v algebre kompaktnykh operatorov”, Tr. MIAN, 306, 2019, 227–234 | Zbl
[28] A. Sergeev, “Quantum differentials and function spaces”, Sb. Trudov konferentsii posv. 70-letiyu N. Vasilevskogo, Birkhauser, 2020 (to appear) | Zbl
[29] A. Sergeev, “Quantum Hall effect and non-commutative geometry”, Sb. Trudov konferentsii, posv. pamyati B.Yu. Sternina, Birkhauser, 2020 (to appear) | Zbl
[30] A. G. Sergeev, “V poiskakh beskonechnomernoi kelerovoi geometrii”, UMN, 75:2 (2020), 133–184 | MR | Zbl
[31] A. Sergeev, “Universal Teichmuller space as a non-trivial example of infinite-dimensional complex manifolds”, Handbook of Teichmüller Theory, v. 7, Lect. Math. Theor. Phys., 30, EMS, Berlin, 2020, 195–213 | Zbl
[32] A. G. Sergeev, “Magnitnaya teoriya Blokha i nekommutativnaya geometriya”, Tr. MIAN, 279, 2012, 193–205 | Zbl
[33] A. G. Sergeev, “Drobnyi kvantovyi effekt Kholla s tochki zreniya nekommutativnoi geometrii”, Tr. Seminara po vektornomu i tenzornomu analizu, 28, MGU, M., 2012, 250–270
[34] I. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973
[35] I. Stein, G. Veis, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974
[36] D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. den Nijs, “Quantized Hall conductance in a twodimensional periodic potential”, Phys. Rev. Lett., 49:6 (1982), 405–408 | DOI
[37] J. Xia, “Geometric invariants of the quantum Hall effect”, Commun. Math. Phys., 119 (1988), 29–50 | DOI | MR | Zbl