Some papers

• P.Exner, A.Laptev and M.Usman, On some sharp spectral inequalities for Schrödinger operators on semiaxis, accepted for publ. in CMP.

• J.-C. Cuenin, A.Laptev and C.Tretter Eigenvalue estimates for non-selfadjoint Dirac operators on the real line, accepted for publ. in AHP.

• 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, 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.

• 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, Birkh?user Verlag Basel/Switzerland.

• A. Laptev and T. Weidl, Recent results on Lieb-Thirring inequalities, Journ?es "?quations aux D?riv?es 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.