Some papers

• R.Frank, B.Helffer and A.Laptev, Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups, accepted by PAFA.

• R.Frank, T.Hoffmann-Ostenhof, A.Laptev and J.P.Solovej, Hardy inequalities for large fermionic systems, JST, 14, (2) (2024) 805-835.

• C.Cazacu, D.Krejcirik, N.Lam and A.Laptev, Hardy inequalities for magnetic p-Laplacians, Nonlinearity, 37, (3) (2024), 27p.

• A.Ilyin, A.Laptev and T.Weinmann, Lieb--Thirring inequalities on Manifolds with constant negative curvature, JGA, 34:62 (2024), 1-17.

• R.L. Frank, A.Laptev and L.Read, Weighted CLR type bounds in two dimensions, TAMS, 377 (5) (2024), 3357-3371.

• A.Laptev and O.Safronov, Absolutely continuous spectrum of a typical Schrödinger operator with an operator valued potential, St. Petersbg. Math. J., 35 (1) (2024).

• T.Hoffmann-Ostenhof, A.Laptev and I.Shcherbakov, Hardy and Sobolev inequalities on antisymmetric functions, Bull. Math. Sci., 14 (1) (2024), 18p.

• A.Ilyin and A.Laptev, Magnetic Lieb--Thirring inequalities on the torus, J. Spectr. Theory 13,(3) (2023), 1111--1127.

• D.Krejcirik, A.Laptev and F.Stampach, Spectral enclosures and stability for non-self-adjoint discrete Schrödinger operators on the half-line, Bulletin of LMS, 54 (6) (2022), 2379-2403.

• R.Frank, A.Laptev and T.Weidl, An improved one-dimensional Hardy inequality, Journal of Mathematical Sciences, 268 (3) (2022), 323-342, (DOI 10.1007/s10958-022-06199-8).

• A.Laptev, L. Reed and L.Schimmer, Calogero type bounds in two dimensions, ARMA, 245, (3), (2022), 1491-1505.

• A.Laptev, M.Loss and L.Schimmer, On a conjecture by Hundertmark and Simon, Annales Henri Poincare, 23 (2022), 4057--4067; doi:10.1007/s00023-022-01169-x.

• A.Laptev and L.Schimmer, A sharp Lieb--Thirring inequality for functional difference operators, SIGMA 17 (2021), 105, 10 pages.

• A.Laptev, On factorization of a class of Schrödinger operators, Complex Variables and Elliptic Equations, 66, (6-7) (2021) 1100--1107; Special Issue Dedicated to the 110th Anniversary of S.L. Sobolev.

• A.Laptev and T.Weth, Spectral properties of the logarithmic Laplacian, Analysis and Mathematical Physics, 11, Article number: 133 (2021), 10.1007/s13324-021-00527-y.

• D.Bonheure, J.Dolbeault, M.J.Esteban, A.Laptev and M.Loss, Inequalities involving Aharonov-Bohm magnetic potentias in dimensions 2 and 3, Reviews in Mathematical Physics, 33: 2150006 (2021).

• Th. Hoffmann-Ostenhof and A.Laptev, Hardy inequality for antisymmetric functions, Funktsional. Anal. i Prilozhen., 55 (2), (2021), 55-64.

• O. Ibrogimov, D. Krejcirik, A. Laptev, Sharp bounds for eigenvalues of biharmonic operators with complex potentials in low dimensions, Mathematische Nachrichten, 294, n.7 (2021), 1333-1349,

• Ilyin, A.Laptev and S.Zelik, On Lieb-Thirring constant on the sphere and on the torus, JFA, 279, n.12 (2020), doi.org/10.1016/j.jfa.2020.108784.

• A.Laptev, L. Schimmer and L. Takhtajan Weyl asymptotics for perturbed functional difference operators, J. Math. Phys. (2019); doi: 10.1063/1.5093401.

• D.Bonheure, J.Dolbeault, M.J.Esteban, A.Laptev and M.Loss, Symmetry Results in Two-Dimensional Inequalities for Aharonov-Bohm Magnetic Fields, CMP, (2019) DOI 10.1007/s00220-019-03560-y.

• A. Ilyin and A.Laptev, Berezin--Li--Yau inequalities on domains on the sphere, JMAA, 473 (2) (2019), 1253--1269.

• J.Dolbeault, M.J.Esteban, A.Laptev and M.Loss, Magnetic rings, Journal of Mathematical Physics 59, 2018.

• A. Hassannezhad and A.Laptev, Eigenvalue bounds of mixed Steklov problems, Communications in Contemporary Mathematics (2017), doi.org/10.1142/S0219199719500081.

• M.Ashbaugh, F.Gesztesy, A.Laptev, M.Mitrea and S.Sukhtaiev, A Bound for the Eigenvalue Counting for Krein--von Neumann and Friedrichs Extensions, Adv. Math. 304 (2017), 1108--1155.

• A.Laptev, L. Schimmer and L. Takhtajan, Weyl-type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves, Geom. Funct. Anal., 26, 2016, 288-305.

• A. Ilyin, A. Laptev, M. Loss and S. Zelik, One-dimensional interpolation inequalities, Carlson--Landau inequalities and magnetic Schrödinger operators , Int. Math. Res. Notices, 4 (2016), 1190--1222.

• L. Kapitanski and A. Laptev, On continuous and discrete Hardy inequalities, J. Spectr. Theory, 6, no. 4 (2016), 837--858.

• F.Gesztesy, A.Laptev, M. Mitrea and S.Sukhtaev, A bound for the eigenvalue counting function for higher-order Krein Laplacians on open sets, Proceedings of QMATH12, Berlin, 2013.

• Th. Hoffmann-Ostenhof and A. Laptev, Hardy inequalities with homogenuous weights, J. Funct. Anal., 268 (2015) 3278--3289.

• A. Ilyin, A. Laptev and S. Zelik, Sharp interpolation inequalities for discrete operators and applications, Bull. Math. Sci. 5, no. 1 (2015).

• J. Dolbeault, M.J. Esteban, A. Laptev and M. Loss One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: Remarks on duality and flows, JLMS, II. Ser. 90, (2014) no. 2, 525-550.

• J. Dolbeault, M.J. Esteban, A. Laptev and M. Loss Spectral properties of Schrödinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates, C. R., Math., Acad. Sci. Paris 351, (2013) no. 11-12, 437-440.

• J. Dolbeault, M.J. Esteban and A. Laptev Spectral estimates on the sphere, Analysis &PDE, 7, (2014) no. 2, 435-460.

• P.Exner, A.Laptev and M.Usman, On some sharp spectral inequalities for Schrödinger operators on semiaxis, Commun. Math. Phys. 326, (2014) no. 2, 531--541.

• J.-C. Cuenin, A.Laptev and C.Tretter Eigenvalue estimates for non-selfadjoint Dirac operators on the real line, Ann. Henri Poincare, 15, (2014) no. 4, 707--736.

• H.Kovarik and A. Laptev, Hardy inequalities for Robin Laplacians, JFA, 262, (2012) no. 12, 4972-4985.

• A.Laptev and M.Solomyak, On spectral estimates for two-dimensional Schrödinger operators, accepted for publ. in J. Spectr. Theory.

• A. Laptev and M.Solomyak, On the negative spectrum of the two-dimensional Schrödinger operator with radial potential, Comm. Math. Phys. 314 (2012), n.1, 229-241.

• A. Laptev, Spectral inequalities for Partial Differential Equations and their applications, Proceedings of ICCM2010 in Beijing, AMS/IP Studies in Advanced Mathematics, 51, (2011).

• L. Geisinger, A. Laptev and T.Weidl, Geometrical versions of improved Berezin-Li-Yau inequalities, J. Spectr. Theory (2011), no. 1, 87-109.

• R.Frank and A.Laptev and R. Seiringer), A Sharp Bound on Eigenvalues of Schrödinger Operators on the Half-line with Complex-valued Potentials, Operator Theory: Advances and Applications, vol. 214 (2010), 39-44.

• R.Frank, A.Laptev, Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group, Int. Math. Res. Not. (2010) no.15, 2889-2902.

• 63. F.Avkhadiev and A.Laptev, On a sharp Hardy inequality for convex domains, Around the research of Vladimir Maz'ya. I. Function Spaces. Dordrecht: Springer; International Mathematical Series (New York) 12, (2010) 1-12.

• A.Laptev and O. Safronov, Eigenvalue estimates for Schrödinger operators with complex potentials, Comm. Math. Phys. 292 (2009), no. 1, 29-54.

• J. Dolbeault, A. Laptev and M. Loss, Lieb-Thirring inequalities with improved constants, JEMS, 10 (2008) no 4. 1121-1126.

• A.M. Hansson and A. Laptev, Sharp spectral inequalities for the Heisenberg Laplacian, Groups and Analysis, The legacy of Hermann Weyl, Cambridge University Press, (2008) 100-115.

• R.Frank and A.Laptev, Spectral inequalities for Schrödinger operators with surface potentials, Spectral theory of differential operators, Amer. Math. Soc.Transl. Ser. 2, 225, Amer. Math. Soc., Providence, RI (2008) 91-102.

• M.Hoffmann-Ostenhof, Th.Hoffmann-Ostenhof, A.Laptev and J.Tidblom, Many-particle Hardy inequalities, J. Lond. Math. Soc. (2) 77 (2008), no. 1, 99-114.

• A.Laptev and A.Sobolev, Hardy inequalities for simply connected planar domains, Spectral theory of differential operators, Amer. Math. Soc. Transl. Ser. 2, 225, Amer. Math. Soc., Providence, RI, 2008) 133-140.

• R.Frank, A.Laptev and S.Molchanov, Eigenvalue estimates for magnetic Schrödinger operators in domains, Proc. Amer. Math. Soc. 136 (2008), no. 12, 4245-4255.

• A. Laptev, R. Shterenberg and V. Sukhanov, Inverse spectral problems for Schrödinger operators with energy depending potentials, CRM Proceedings & Lecture Notes, 42 (2007), 341-352.

• R. Frank A., Laptev, E.H. Lieb and R. Seiringer , Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials, Letters in Math. Physics, 77 (2006), 309-316.

• A. Laptev, R. Shterenberg, V. Sukhanov and J.Östensson, Reflectionless potentials for an ordinary differential operator of order four, Inverse Problems 22 (2006), 135-153.

• J. Hoppe, A. Laptev and J.Östensson, Solitons and the Removal of Eigenvalues for Fourth Order Differential Operators, IMRN, 2006, ID 85050.

• E. Langmann, A. Laptev and C. Paufler, Singular factorizations, self-adjoint extensions and applications to quantum many-body physics., J.Phys. A: Math.Gen. 39 (2006), 1057-1071.

• A. Laptev, Spectral inequalities and their applications, Lecture Notes, Warwick, April 2005.

• A. Laptev, S. Naboko and O. Safronov, Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials, Comm. Math. Physics, 253 (2005), 611-631.

• A. Laptev, S. Naboko and O. Safronov, A Szegö condition for a multidimensional Schrödinger operator, J.Func.Anal., 219 (2005), 285-305.

• A. Balinsky, A. Laptev and A. Sobolev, Generalized Hardy inequality for the magnetic Dirichlet forms, Journal of Statistical Physics, 116 (2004), 507-521.

• S. Chanillo, B. Helffer and A. Laptev, Non linear eigenvalues and analytic hypoellipticity, J. Func. Anal., 209 (2004), 425-443.

• A. Laptev, S. Naboko and O. Safronov, On new relations between spectral properties of Jacobi matrices and their coefficients, Comm. Math. Physics., 241 (2003), 91-110.

• M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and A. Laptev, A geometrical version of Hardy's inequality, J. Funct. Anal., 189 (2002), 539-548.

• A. Laptev and T. Weidl, Sharp Lieb-Thirring inequalities in high dimentions, Acta Mathematica, 184 (2000), 87-111.

• D. Hundertmark, A. Laptev and T. Weidl, New bounds on the Lieb-Thirring constants, Invent. math., 140 (2000), 693-704.

• A. Laptev and T. Weidl, Hardy inequalities for magnetic Dirichlet forms, Operator Theory: Advances and Applications, 108, p. 299-305, 1999, Birkhauser Verlag Basel/Switzerland.

• A. Laptev and T. Weidl, Recent results on Lieb-Thirring inequalities, Equations aux derivees partielles (La Chapelle sur Erdre, 2000), Exp. No. XX, 14 pp., Univ. Nantes, Nantes, 2000.

• A. Laptev, The negative spectrum of a class of two-dimensional Schrödinger operators with spherically symmetric potentials, Funct. Anal. Appl, 34, (2000), No. 4, 305-307.

• A. Laptev and I.M. Sigal Global Fourier Integral Operators and semiclassical asymptotics, Review of Math. Phys., 12, (2000), No. 5, 749-766.

• A. Laptev and Yu. Netrusov, On the negative eigenvalues of a class of Schrödinger operators., Amer. Math. Soc., Providence, Differential operators and spectral theory, Amer. Math. Soc. Transl. Ser. 2 189 (1999), 173--186.

• A. Laptev and Yu. Safarov, Szegö type limit theorems, J. Funct. Anal., 138 (1996), 544-559.

• A. Laptev, Dirichlet and Neumann Eigenvalue Problems on Domains in Euclidean Spaces, J. Funct. Anal., 151 (1997), 531-545.

• A. Laptev and Yu. Safarov, A Generalization of the Berezin-Lieb Inequality, Amer. Math. Soc. Transl., (2) 175 (1996), 69-79.

• A. Laptev, Yu. Safarov and D. Vassiliev, On global representation of Lagrangian distributions and solutions of hyperbolic equations, Comm. Pure Appl. Math., (II) 47 (1994), 1411-1456.

• A. Laptev, Spectral asymptotic behavior of a class of integral operators, Mat. Zametki, 16 (1974), 741-750.