- Spectral theory of differential and integral operators,
- Toeplitz operators
Main papers (> 75 in total)
- Distribution of the discrete spectrum of singular differential operators. (Russian) Dokl. Akad. Nauk SSSR 202 (1972), 1012–1015.
- Near-similarity of operators and the spectral asymptotic behavior of pseudodifferential operators on the circle. (Russian) Trudy Moskov. Mat. Obshch. 36 (1978), 59–84,
- Spectral asymptotic behavior of elliptic systems. (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), 255–271 (with Solomyak, M. Z.; Shubin, M. A.)
- Spectral theory of differential operators. (Russian) Current problems in mathematics. Fundamental directions, Vol. 64 (Russian), 5–248, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989; English translation: Springer, Encyclopaedia of Mathematical Sciences , vol.64, 1994
- Index formulae for pseudodifferential operators with discontinuous symbols. Ann. Global Anal. Geom. 15 (1997), no. 1, 71–100. Domination of semigroups and estimates for eigenvalues. (Russian) Algebra i Analiz 12 (2000), no. 5, 158—177 ( with Melgaard, M.)
- Eigenvalue asymptotics for weakly perturbed Dirac and Schrödinger operators with constant magnetic fields of full rank. Comm. Partial Differential Equations 28 (2003), no. 3-4, 697–736.
- Regularisation of secondary characteristic classes and unusual index formulas for operator-valued symbols. Nonlinear hyperbolic equations, spectral theory, and wavelet transformations, 419–437, Oper. Theory Adv. Appl., 145, Adv. Partial Differ. Equ. (Basel), Birkhäuser, Basel, 2003. ( with Agranovich, M. S.);
- Spectral boundary value problems for a Dirac system with singular potential. (Russian) Algebra i Analiz 16 (2004), no. 1, 33—69; ( with Melgaard, M. )
- Schrödinger operators with singular potentials. Stationary partial differential equations. Vol. II, 407–517, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2005. (with Shirokov, N.)
- Infiniteness of zero modes for the Pauli operator with singular magnetic field. J. Funct. Anal. 233 (2006), no. 1, 135–172. ( with Tashchiyan, G.)
- On the spectral properties of the perturbed Landau Hamiltonian. Comm. Partial Differential Equations 33 (2008), no. 4-6, 1048–1081. ( with Sobolev, Alexander V).
- Discrete spectrum distribution of the Landau operator perturbed by an expanding electric potential. Spectral theory of differential operators, 169–190, Amer. Math. Soc. Transl. Ser. 2, 225, Adv. Math. Sci., 62, Amer. Math. Soc., Providence, RI, 2008.
- On lower eigenvalue bounds for Toeplitz operators with radial symbols in Bergman spaces. J. Spectr. Theory 1 (2011), no. 3, 299–325. (with Vasilevski, N.)
- Toeplitz operators defined by sesquilinear forms: Fock space case. J. Funct. Anal. 267 (2014), no. 11, 4399–4430. (with Shirokov, N. ) Some weighted estimates for the ∂¯¯¯-equation and a finite rank theorem for Toeplitz operators in the Fock space. Proc. Lond. Math. Soc. (3) 109 (2014), no. 5, 1281–1303. (with Vasilevski, N.)
- Toeplitz operators in the Herglotz space. Integral Equations Operator Theory 86 (2016), no. 3, 409–438. (with Nursultanov, M.)
- Eigenvalue asymptotics for the Sturm-Liouville operator with potential having a strong local negative singularity. Opuscula Math. 37 (2017), no. 1, 109–139. ( with Tashchiyan, G) .
- Eigenvalue asymptotics for potential type operators on Lipschitz surfaces of codimension greater than 1. Opuscula Math. 38 (2018), no. 5, 733–758.
- Methods of investigation of discrete spectrum for operators of mathematical physics, Master students
- Editor in Chief: American Journal of Mathematical Analysis
- Member of editorial board: Journal of Spectral Theory
- Member of editorial board: Boletín de la Sociedad Matemática Mexicana Journal of Mathematical Sciences (Springer)