Pade approximations and their generalizations, noncommutative Grassmannian sigma models; holomorphic solutions of integrable equations.
Main publications:
A. V. Komlov, S. P. Suetin, “An asymptotic formula for polynomials orthonormal with respect to a varying weight. II”, Sb. Math., 205:9 (2014), 1334–1356
A. V. Komlov, S. P. Suetin, “Asimptoticheskaya formula dlya polinomov, ortonormirovannykh otnositelno peremennogo vesa”, Tr. MMO, 73, no. 2, MTsNMO, M., 2012, 175–200
A. V. Komlov, “On the poles of Picard potentials”, Trans. Moscow Math. Soc., 71 (2010), 241–250
A. V. Komlov, “Noncommutative Grassmannian $U(1)$ sigma model and a Bargmann–Fock space”, Theoret. and Math. Phys., 153:3 (2007), 1643–1651
A. V. Komlov, R. V. Palvelev, “Zeros of discriminants constructed from Hermite–Padé polynomials of an algebraic function and their relation to branch points”, Mat. Sb. (to appear)
2.
A. V. Komlov, “The polynomial Hermite-Padé $m$-system for meromorphic functions on a compact Riemann surface”, Sb. Math., 212:12 (2021), 1694–1729
3.
A. V. Komlov, “Polynomial Hermite–Padé $m$-system and reconstruction of the values of algebraic functions”, Trends Math., 12, 2021, 113–121;
A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706
5.
A. V. Komlov, N. G. Kruzhilin, R. V. Palvelev, S. P. Suetin, “Convergence of Shafer quadratic approximants”, Russian Math. Surveys, 71:2 (2016), 373–375
6.
A. V. Komlov, S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials”, Russian Math. Surveys, 70:6 (2015), 1179–1181
7.
A. V. Komlov, S. P. Suetin, “Strong asymptotics of two-point Padé approximants for power-like multivalued functions”, Dokl. Math., 89:2 (2014), 165–168
8.
A. V. Komlov, S. P. Suetin, “An asymptotic formula for polynomials orthonormal with respect to a varying weight. II”, Sb. Math., 205:9 (2014), 1334–1356
9.
A. V. Komlov, S. P. Suetin, “An asymptotic formula for a two-point analogue of Jacobi polynomials”, Russian Math. Surveys, 68:4 (2013), 779–781
10.
A. V. Komlov, S. P. Suetin, “Widom's formula for the leading coefficient of a polynomial which is orthonormal with respect to a varying weight”, Russian Math. Surveys, 67:1 (2012), 183–185
11.
A. V. Komlov, S. P. Suetin, “Asimptoticheskaya formula dlya polinomov, ortonormirovannykh otnositelno peremennogo vesa”, Tr. MMO, 73, no. 2, MTsNMO, M., 2012, 175–200
A. V. Komlov, S. P. Suetin, “Leading coefficients asymptotics for orthonormal polynomials with respect to varying weight”, 4th Russian-Armenian workshop on mathematical physics, complex analysis and related topics (Russia, Krasnoyarsk, September 9–16, 2012), Abstracts, Siberian Federal University, Krasnoyarsk, 2012, 26–29pdf (in Russian)
13.
A. V. Komlov, “On the poles of Picard potentials”, Trans. Moscow Math. Soc., 71 (2010), 241–250
14.
A. V. Komlov, “Estimates of the Gevrey classes of scattering data for polynomial potentials”, Russian Math. Surveys, 63:4 (2008), 788–789
15.
A. V. Komlov, “Noncommutative Grassmannian $U(1)$ sigma model and a Bargmann–Fock space”, Theoret. and Math. Phys., 153:3 (2007), 1643–1651
16.
A. Komlov, “Noncommutative Grassmannian $U(1)$ sigma-model and Bargmann-Fock space”, XXV Workshop on Geometric Methods in Physics (Bialowieza, Poland, 2–8 July, 2006), J. Geom. Symmetry Phys., 10, 2007, 41–49
17.
Analiz i matematicheskaya fizika, Sbornik statei. K 70-letiyu so dnya rozhdeniya professora Armena Glebovicha Sergeeva, Trudy MIAN, 311, ed. S. Yu. Nemirovskii, A. V. Komlov, MIAN, M., 2020 , 281 pp.
Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, ed. S. Yu. Nemirovski, A. V. Komlov, 2020, 281 с. http://mi.mathnet.ru/book1806
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