профессор, доктор физико-математических наук
Fields of Research
- 1D inverse spectral theory for Schrodinger operator with periodic potentials, Sturm-Liouville problems on finite intervals, for the difference operators, Schrodinger operator with matrix-valued potentials, perturbed harmonic oscillator.
- Integrable systems (KdV and non-linear Schrodinger equation), a priori estimates for integrable systems, symplectic coordinates.
- Geometric function theory (harmonic and functional analysis, geometric function theory, the Lowner equation for the conformal mapping associated with quasimomentum)
- Scattering theory including few body systems in external fields.
- Schrodinger operators on periodic media, including graphs, and nano-media.
- Theory of resonances and inverse resonance scattering.
- Multidimensional inverse problems for Schrodinger operators on the lattice.
Selected visiting positions during 2011-14
- 2014 , KTH, Stockholm, Sweden
- 2013: Aarhus University, Denmark, Potsdam University, Germany, Mittag-Leffler Institute, Sweden; Tsukuba University, Japan; Humboldt University, Germany
- 2012: Tsukuba University, Japan; Potsdam University, Germany, Aarhus University, Denmark, Malmo University, Sweden,
- 2011; Mittag-Leffler Institute, Sweden; University Bordeaux 1, France; Humboldt University, Berlin; University of Barcelona, Spain; Ecole Polytechnique, Palaiseau, France,
Conferences and workshops
2013
- Linkoping, Sweden, Conference on Inverse Problems and Application, April 2-6,
- May 28-June 1, St. Petersburg, (Diffraction Days),
- Q-Math, Berlin, Sep. 10-13,
- RIMS, Kyoto, Japan, “Spectral and Scattering Theory and Related Topics”, 11-13 Dec.,
- Bielefeld, Germany, “Mathematical Technology of Networks” 3-7 Dec.,
2012
- August 5-12, Aalborg, International Congress on Mathematical Physics,
- May 28-June 1, St. Petersburg, (Diffraction Days),
2011
- December 8-13, Mittag-Leffler Institute, (Geometric analysis and mathematical physics),
- September 27-29, Paris, Ecole Polytechnique, (Inverse Problems and Applications) ,
- July 1-6, St. Petersburg, (Spectral Theory)
- May 30-June 4, Barcelona, (Hilbert Spaces of Entire Functions and Spectral Theory),
- February 16-20, Kyoto, RIMS, (Spectral and Scattering Theory and Related Topics).
Список публикаций (.pdf)
[112] Korotyaev, E.; Saburova, N. Estimates of bands for Laplacians on periodic equilateral metric graphs,
to be published in Proceedings of the American Mathematical Society.
[111] Iantchenko, A.; Korotyaev, E. Resonances for the radial Dirac operators, to be published in Asymptotic Analysis.
[110] Korotyaev, E. Estimates of 1D resonances in terms of
potentials, to be published in Journal d’Analyse Mathematique.
[109] Korotyaev, E.; Saburova, N. Spectral band localization for Schr\”odinger operators on periodic graphs, to be published in Proceedings of the American Mathematical Society.
[108] Badanin, A.; Korotyaev, E.
Inverse problems and sharp eigenvalue asymptotics for
Euler-Bernoulli operators, Inverse Problem, 31(2015), 055004.
[107] Iantchenko, A.; Korotyaev, E. Resonances for Dirac operators on the half-line, Journal of Mathematical Analysis and Applications, 420 (2014), no 1, 279–-313.
[106] Korotyaev, E.; Saburova, N. Schr\”odinger operators on
periodic discrete graphs, Journal of Mathematical Analysis and Applications, 420 (2014), No 1, 576–611.
[105] Korotyaev, E. Asymptotics of S-matrix for perturbed Hill
operators, Russ. J. Math. Phys. 21(2014), No 1, 46–54.
[104] Badanin, A.; Korotyaev, E. Sharp eigenvalue asymptotics
for fourth order operators on the circle, Journal of Mathematical
Analysis and Applications, 417 (2014), 804–818.
[103] Iantchenko, A.; Korotyaev, E. Resonances for 1D massless
Dirac operators, Journal of Differential Equation, 256(2014),
No 8, 3038 – 3066.
[102] Korotyaev E. Global estimates of resonances for 1D
Dirac operators, Letters in Mathematical Physics, 104 (2014), No 1, 43–53.
[101] Isozaki, H. ; Korotyaev E. Inverse problems, trace
formulae for Schr\”odinger Operators on the lattice, proceedings of
XVIIth International Congress on Mathematical Physics, Aalborg,
Denmark, 6-11 August 2012, Arne Jensen editor, World Scientific,
Singapore, 2014, p. 495–503.
[100] Korotyaev E. Hamiltonian and small action variables for
dNLS on the circle, IMRN, 2013(2013), 2203–2239.
[99] Badanin, A.; Korotyaev, E. Third order operator with
periodic coefficients on the real line, Algebra i Analiz, 25(2013), No 5, 1–31.
[98] Badanin, A.; Korotyaev, E. Trace formula for fourth
order operators on the circle, Dynamics of PDE, 10(2013), No.4, 343–352.
[97] Korotyaev E. Sharp asymptotics of the quasimomentum,
Asymptotic Analysis, 80(2012), no 3-4, 269–287.
[96] Korotyaev, E.; Schmidt, K. On the resonances and
eigenvalues for a 1D half-crystal with localized impurity, J. Reine
Angew. Math. 2012, Issue 670, 217–248.
[95] Badanin, A.; Korotyaev, E. Spectral asymptotics for the
third order operator with periodic coefficients, J. Differential
Equations, 253 (2012), No 11, 3113–3146.
[94] Isozaki, H. ; Korotyaev E. Inverse Problems,
Trace formulae for discrete Schr\”odinger Operators, Annales Henri
Poincare, 13(2012), No 4 , 751–788.
[93] Badanin, A.; Korotyaev, E. Even order periodic operators
on the real line, IMRN, 2012(2012), No 5, 1143–1194.
[92] Iantchenko, A.; Korotyaev, E. Resonances for periodic
Jacobi operators with finitely supported perturbations, Journal of
Mathematical Analysis and Applications, 388( 2012), No 2,
1239–1253.
[91] Iantchenko, A.; Korotyaev, E. Periodic Jacobi operator with
finitely supported perturbations: the inverse resonance problem, J.
Differential Equations, 252(2012), No 3, 2823–2844.
[90] Isozaki, H.; Korotyaev, E. Trace formulas for
Schr\”odinger operators, from the view point of complex analysis,
Proceeding of RIMS Symposium Febr. 16-18, 2011 (Kyoto, Japan),
2011, p. 16-32.
[89] Iantchenko, A.; Korotyaev, E. Periodic Jacobi operator with
finitely supported perturbation on the half-lattice, Inverse
Problems, 27(2011), No 11, 26 pp.
[88] Korotyaev, E. Inverse resonance scattering for Jacobi
operators, Rus. J. Math. Phys. 18(2011), No. 4, pp. 427–439.
[87] Korotyaev, E. Resonance theory for perturbed Hill
operator, Asymp. Anal. 74(2011), No 3-4, 199–227.
[86] Korotyaev, E. Estimates for solutions of KDV on the
phase space of periodic distributions in terms of action variables,
Discrete Contin. Dyn. Syst. 30(2011), no. 1, 219–225.
[85] Korotyaev, E.; Kargaev, P. Estimates for periodic
Zakharov-Shabat operators, J. Differential Equations, 249(2010),
76–93.
[84] Korotyaev, E.; Kutsenko, A. Zigzag nanoribbons in external
electric and magnetic fields. Int. J. Comput. Sci. Math. 3 (2010),
no. 1-2, 168–191.
[83] Badanin, A.; Korotyaev, E. . A magnetic Schr\”odinger
operator on a periodic graph. Mat. Sb. 201 (2010), no. 10,
3–46.
[82] Badanin, A.; Korotyaev, E. Spectral estimates for a
periodic fourth-order operator. St. Petersburg Math. J. 22 (2011)
703–736.
[81] Iantchenko, A.; Korotyaev, E. Schr\”odinger operator on
the zigzag half-nanotube in magnetic field. Math. Model. Nat.
Phenom. 5(2010), No. 4, 175–197.
[80] Korotyaev, E.; Kutsenko, A. Zigzag nanoribbons in external
electric Fields, Asympt. Anal. 66(2010), no 3-4, 187–206.
[79] Korotyaev, E.; Kutsenko, A. Zigzag and armchair nanotubes
in external fields, “Differential Equations: Advances in
Mathematics Research, Volume 10 (2010) Nova Science Publishers, Inc.
273– 302.
[78] Korotyaev, E. Conformal spectral theory for the
monodromy matrix, Trans. Amer. Math. Soc. 362 (2010), 3435–3462.
[77] Chelkak, D.; Korotyaev, E. Weyl-Titchmarsh functions of
vector-valued Sturm-Liouville operators on the unit interval, Journal
Func. Anal., 257 (2009), 1546–1588.
[76] Korotyaev, E.; Kutsenko, A. Borg-type uniqueness Theorems
for periodic Jacobi operators with matrix-valued coefficients, Proc.
Amer. Math. Soc. 137 (2009), No 6, 1989–1996.
[75] Chelkak, D.; Korotyaev, E.
The inverse Sturm-Liouville problem with mixed boundary conditions,
St. Petersburg Math. Journal. 21(2009), no 5, 114–137.
[74] Korotyaev, E. Remark on estimate of a potential in terms
of eigenvalues of the Sturm-Liouville operator, Modern Physics
Letters B., 22(2008), No. 23, 2177–2180.
[73] Korotyaev, E. Spectral estimates for matrix-valued
periodic Dirac operators, Asymptotic Analysis, 59(2008), no. 3-4,
195–225.
[72] Korotyaev, E. A priori estimates for the Hill and Dirac
operators, Russ. J. Math. Phys.,15(2008), No. 3, pp. 320–331.
[71] Korotyaev, E.; Kutsenko, A. Lyapunov functions of
periodic matrix-valued Jacobi operators, Spectral theory of
differential operators, 117–131, Amer. Math. Soc. Transl. Ser. 2,
225, Amer. Math. Soc., Providence, RI, 2008.
[70] Korotyaev, E. Effective masses for zigzag nanotubes in
magnetic fields, Lett. Math. Phys., 83 (2008), No 1, 83-95.
[69]
Korotyaev, E.; Kutsenko, A. Marchenko-Ostrovski mappings for
periodic Jacobi matrices, Russ. J. Math. Phys. 14(2007), no 4, 448-452.
[68] Korotyaev, E.; Lobanov, I. Schrodinger Operators on
Zigzag Nanotubes, Annales Henri Poincare, 8(2007), no.6,
1151–1176.
[67] Chelkak, D.; Korotyaev, E. The inverse problem for
perturbed harmonic oscillator on the half-line with Dirichlet
boundary conditions, Annales Henri Poincare, 8(2007), no.6,
1115–1150.
[66]
Chelkak, D.; Korotyaev, E. Parametrization of the isospectral set
for the vector-valued Sturm-Liouville problem, J. Funct. Anal.,
241(2006), 359-373.
[65]
Korotyaev, E. Gap-length mapping for periodic Jacobi
matrices, Russ. J. Math. Phys. 13(2006), no.1, 64-69.
[64] Chelkak, D.; Korotyaev, E. Spectral estimates for
Schodinger operators with periodic matrix potentials on the real
line. Int. Math. Res. Not. 2006, Art. ID 60314, 41 pp.
[63] Korotyaev, E. Estimates for the Hill operator. II. J.
Differential Equations 223 (2006), no. 2, 229–260.
[62] Badanin, A.; Bruning, J.; Korotyaev, E. The Lyapunov
function for Schrodinger operators with a periodic 2×2 matrix
potential. J. Funct. Anal. 234 (2006), no. 1, 106–126.
[61] Korotyaev, E.; Kutsenko, A. Inverse problem for
the discrete 1D Schr\”odinger operator with small periodic
potentials. Comm. Math. Phys. 261 (2006), no. 3, 673–692.
[60] Klein, M.; Korotyaev, E.; Pokrovski, A.
Spectral asymptotics of the harmonic oscillator perturbed by bounded potentials.
Ann. Henri Poincar\’e 6(2005), no. 4, 747–789.
[59] Badanin, A.; Korotyaev, E. Spectral asymptotics
for periodic fourth-order operators. Int. Math. Res. Not. 2005, no.
45, 2775–2814.
[58] Korotyaev, E. Schr\”odinger operator with a junction of two
1-dimensional periodic potentials. Asymptot. Anal. 45 (2005), no.
1-2, 73–97.
[57] Korotyaev, E. Inverse problem and estimates for
periodic Zakharov-Shabat systems. J. Reine Angew. Math. 583 (2005),
87–115.
[56] Korotyaev, E. Inverse resonance scattering on the real
line. Inverse Problems 21 (2005), no. 1, 325–341.
[55] Kargaev, P.; Korotyaev, E. Identities for the Dirichlet
integral of subharmonic functions from the Cartright class. Complex
Var. Theory Appl. 50 (2005), no. 1, 35–50.
[54]
Korotyaev, E.; Kutsenko, A. An inverse problem for the
discrete periodic Schr\”odinger operator. (Russian) Zap. Nauchn.
Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 315 (2004),
Issled. po Linein. Oper. i Teor. Funkts. 32, 96–101, 157
[53]
Korotyaev, E. Stability for inverse resonance problem. Int.
Math. Res. Not. 2004, no. 73, 3927–3936.
[52]
Korotyaev, E. Inverse spectral problem for the periodic
Camassa-Holm equation. J. Nonlinear Math. Phys. 11 (2004), no. 4,
499–507.
[51]
Korotyaev, E.; Pushnitski, A. A trace formula and high-energy
spectral asymptotics for the perturbed Landau Hamiltonian. J. Funct.
Anal. 217 (2004), no. 1, 221–248.
[50] Chelkak, D.; Kargaev, P.; Korotyaev, E. Inverse problem
for harmonic oscillator perturbed by potential, characterization.
Comm. Math. Phys. 249 (2004), no. 1, 133–196.
[49] Chelkak, D.; Kargaev, P.; Korotyaev, E. Inverse problem
for harmonic oscillator perturbed by potential. Inverse problems and
spectral theory, 93–102, Contemp. Math., 348, Amer. Math. Soc.,
Providence, RI, 2004.
[48] Korotyaev, E. Inverse resonance scattering on the half
line. Asymptot. Anal. 37 (2004), no. 3-4, 215–226.
[47] Badanin, A.; Klein, M.; Korotyaev, E. The
Marchenko-Ostrovski mapping and the trace formula for the
Camassa-Holm equation. J. Funct. Anal. 203 (2003), no. 2, 494–518.
[46] Korotyaev, E.; Pushnitski, A. On the high-energy
asymptotics of the integrated density of states. Bull. London Math.
Soc. 35 (2003), no. 6, 770–776.
[45] Chelkak, Dmitri; Kargaev, Pavel; Korotyaev, Evgeni An
inverse problem for an harmonic oscillator perturbed by potential:
uniqueness. Lett. Math. Phys. 64 (2003), no. 1, 7–21.
[44] Korotyaev, E. Characterization of the spectrum of
Schr\”odinger operators with periodic distributions.
Int. Math. Res. Not. 2003, no. 37, 2019–2031.
[43] Korotyaev, E.; Pushnitski, A. Trace formulae and high
energy asymptotics for the Stark operator. Comm. Partial
Differential Equations 28 (2003), no. 3-4, 817–842.
[42] Korotyaev, E.; Krasovsky, I. V. Spectral estimates for
periodic Jacobi matrices. Comm. Math. Phys. 234 (2003), no. 3,
517–532.
[41] Korotyaev, E. Periodic “weighted” operators. J.
Differential Equations 189 (2003), no. 2, 461–486.
[40] Korotyaev, E. Invariance principle for inverse problems.
Int. Math. Res. Not. 2002, no. 38, 2007–2020.
[39]
Korotyaev, E. Marchenko-Ostrovki mapping for periodic
Zakharov-Shabat systems. J. Differential Equations 175 (2001), no.
2, 244–274.
[38] Klein, M.; Korotyaev, E. Parametrization of periodic
weighted operators in terms of gap lengths. Inverse Problems 16
(2000), no. 6, 1839–1860.
[37] Korotyaev, E. Lattice dislocations in a $1$-dimensional
model. Comm. Math. Phys. 213 (2000), no. 2, 471–489.
[36] Korotyaev, E. Estimates for the Hill operator. I. J.
Differential Equations 162 (2000), no. 1, 1–26.
[35] Korotyaev, E Inverse problem for periodic “weighted”
operators. J. Funct. Anal. 170 (2000), no. 1, 188–218.
[34] Korotyaev, E. Correction to: “The inverse problem for
the Hill operator. I” [Internat. Math. Res. Notices 1997, no. 3,
113–125]
Internat. Math. Res. Notices 1999, no. 22, 1253.
[33] Kargaev, P.; Korotyaev, E. Erratum: “The inverse problem
for the Hill operator, a direct approach” [Invent. Math. 129 (1997),
no. 3, 567–593], Invent. Math. 138 (1999), no. 1, 227.
[32] Korotyaev, E. L. Inverse problems for the Hill and Dirac
operators. (Russian) Dokl. Akad. Nauk 365 (1999), no. 6, 730–733.
[31] Korotyaev, E. Inverse problem and the trace formula for
the Hill operator. II. Math. Z. 231 (1999), no. 2, 345–368.
[30] Korotyaev, E. Estimates of periodic potentials in terms
of gap lengths. Comm. Math. Phys. 197 (1998), no. 3, 521–526.
[29] Korotyaev, E. L. Uniform estimates for the Hill
operator. (Russian) Dokl. Akad. Nauk 356 (1997), no. 6, 740–743.
[28] Korotyaev, E. L. Estimates for the periodic potential in
terms of effective masses. (Russian) Dokl. Akad. Nauk 356 (1997),
no. 5, 588–591.
[27] Korotyaev, E. The propagation of the waves in periodic
media at large time. Asymptot. Anal. 15 (1997), no. 1, 1–24.
[26] Kargaev, P.; Korotyaev, E. The inverse problem for the
Hill operator, a direct approach. Invent. Math. 129 (1997), no. 3,
567–593.
[25] Korotyaev, E. The estimates of periodic potentials in
terms of effective masses. Comm. Math. Phys. 183 (1997), no. 2,
383–400.
[24] Korotyaev, E. The inverse problem for the Hill operator.
I. Internat. Math. Res. Notices 1997, no. 3, 113–125.
[23] Kargaev, P. P.; Korotyaev, E. L. Inverse problems for the
Hill operator, the direct approach. (Russian) Dokl. Akad. Nauk 351
(1996), no. 2, 158–160.
[22] Korotyaev, E. Metric properties of conformal mappings on
the complex plane with parallel slits. Internat. Math. Res. Notices
1996, no. 10, 493–503.
[21] Korotyaev, E. L.; Pushnitski, A. B. Scattering by an
anisotropic potential in a constant electric field. (Russian) Zap.
Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 230
(1995), Mat. Vopr. Teor. Rasprostr. Voln. 25, 103–114, 295–296
[20] Kargaev, P.; Korotyaev, E. Effective masses and conformal
mappings. Comm. Math. Phys. 169 (1995), no. 3, 597–625.
[19] Korotyaev, E. L.; Firsova, N. E. Diffusion in layered
media for large time values. (Russian) Teoret. Mat. Fiz. 98 (1994),
no. 1, 106–148.
[18] Kargaev, P. P.; Korotyaev, E. L. Effective masses for
the Hill operator, and conformal mappings. (Russian) Dokl. Akad.
Nauk 336 (1994), no. 3, 312–315.
[17] Korotyaev, E. L. Wave propagation in a one-dimensional
periodic medium. (Russian) Dokl. Akad. Nauk 336 (1994), no. 2,
171–174.
[16] Korotyaev, E. L. The Enss method taking into account
anisotropy. (Russian) Dokl. Akad. Nauk 324 (1992), no. 5, 923–927.
[15] Korotyaev, E. L. Some properties of the quasimomentum
of the one-dimensional Hill operator. (Russian) Zap. Nauchn. Sem.
Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 195 (1991), Mat. Vopr.
Teor. Rasprostr. Voln. 21, 48–57.
[14] Korotyaev, E. L. The dynamical Stark effect in a system
of three
particles. (Russian) Teoret. Mat. Fiz. 79 (1989), no. 1, 102–116.
[13] Korotyaev, E. L. On scattering in an exterior homogeneous
and time-periodic magnetic field. (Russian) Mat. Sb. 180 (1989), no.
4, 491–512.
[12] Korotyaev, E. L. On resonance scattering in a pair of
spaces. (Russian) Teoret. Mat. Fiz. 70 (1987), no. 3, 432–442.
[11]
Korotyaev, E. L. On the theory of multiparticle scattering in
an external electric field. (Russian) Mat. Sb. (N.S.) 132(174)
(1987), no. 2, 182–201.
[10] Korotyaev, E. L. Scattering of many particles in an external
electric field. (Russian) Dokl. Akad. Nauk SSSR 284 (1985), no. 1,
107–110.
[9] Korotyaev, E. L. Factorization of a three-particle
$S$-matrix at high energies. (Russian) Teoret. Mat. Fiz. 63 (1985),
no. 3, 388–393.
[8] Korotyaev, E. L. Scattering theory for three-particle
systems with time-periodic pair interactions. (Russian) Teoret. Mat.
Fiz. 62 (1985), no. 2, 242–252.
[7] Korotyaev, E. L. Eigenfunctions of the monodromy operator
of the Schrodinger operator with a potential that is periodic with
respect to time. (Russian) Mat. Sb. (N.S.) 124(166) (1984), no. 3,
431–446.
[6] Korotyaev, E. L. Scattering theory for three particles with pair
potentials that are periodic in time. (Russian) Dokl. Akad. Nauk
SSSR 255 (1980), no. 4, 836–839.
[5] Korotjaev, E. L. On the spectrum of the monodromy operator
of the Schrodinger operator with a potential which is periodic with
respect to time. (Russian) Boundary value problems of mathematical
physics and related questions in the theory of functions, 12. Zap.
Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 96 (1980),
101–104.
[4]
Korotjaev, E. L. The scattering problem for a slowly decreasing
potential that is periodically dependent on time. (Russian) Boundary
value problems of mathematical physics and related questions in the
theory of functions, 11. Zap. Nauchn. Sem. Leningrad. Otdel. Mat.
Inst. Steklov. (LOMI) 84 (1979), 114–116.
[3] Deich, V. G.; Korotjaev, E. L.; Jafaev, D. R. The theory
of potential scattering with account taken of spatial anisotropy.
(Russian) Investigations on linear operators and the theory of
functions, VIII. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst.
Steklov. (LOMI) 73 (1977), 35–51.
[2] Deich, V. G.; Korotjaev, E. L.; Jafaev, D. R. Potential
scattering with allowance for spatial anisotropy. (Russian) Dokl.
Akad. Nauk SSSR 235 (1977), no. 4, 749–752.
[1] Korotjaev, E. L.; Jafaev, D. R. Traces on surfaces in
function classes with dominating mixed derivatives.
Boundary value problems of mathematical physics and related
questions in the theory of functions, 10 (Russian). Zap. Nau\v cn. Sem.
Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 69 (1977), 106–123.