**Analysis:**Partial Differential and Integral Equations, Spectral Theory, Functional Analysis, Complex Variables, Microlocal Analysis, Global Analysis

**Applications:**Fluid Dynamics, Elasticity Theory

- Some remarks on the boundedness of pseudodifferential
operators,
*Math. Nachr.*183, 229-273 (1997). - On two-dimensional singular integral operators with conformal
Carleman shift,
*J. Operator Theory,*37, 263-279 (1997) (with R. Duduchava and A. Saginashvili). - An algebra of integral operators with fixed singularities in kernels,
*Integr. Equat. Oper. Th.*33, 406-425 (1999) (with R. Duduchava and N. Krupnik). - Geometry of higher order relative spectra and projection methods,
*J. Operator Theory,*44, 43-62 (2000). - Semi-elliptic operators generated by vector fields,
*Dissertationes Mathematicae,*409, 96 pp. (2002). - A Riemann-Hilbert problem and the Bernoulli boundary condition in
the variational theory of Stokes waves,
*Annales de l'Institut Henri Poincare (C) Non Linear Analysis,*20, 1, 37-52 (2003) (with J.F. Toland). - Riemann-Hilbert theory for problems with vanishing coefficients that
arise in nonlinear hydrodynamics,
*J. Funct. Analysis,*197, 1, 283-300 (2003) (with J.F. Toland). - Quasi-conformal mappings and periodic spectral problems in dimension
two,
*Journal d'Analyse Mathèmatique,*91, 67-104 (2003) (with A.V. Sobolev). - Spectral pollution and second order relative spectra for self-adjoint
operators,
*IMA J. Numerical Analysis,*24, 3, 393-416 (2004) (with M. Levitin). - The inner variation of an operator and the
essential norms of pointwise
multipliers in function spaces,
*Houston Journal of Mathematics,*31, 3, 841-855 (2005) (with D.E. Edmunds). - Uniqueness results for the Riemann-Hilbert
problem with a vanishing coefficient,
*Integr. Equat. Oper. Th.*56, 115-127 (2006) (with J.A. Virtanen). - Weighted Sobolev theorem with variable exponent for spatial and spherical
potential operators, II,
*Journal of Mathematical Analysis and Applications,*325, 745-751 (2007) (with S. Samko and B.Vakulov). - A remark on the essential spectra of Toeplitz operators with bounded measurable
coefficients,
*Integr. Equat. Oper. Th.*57, 127-132 (2007). - Spectra of Toeplitz operators and compositions of Muckenhoupt weights with
Blaschke products,
*Integr. Equat. Oper. Th.*61, 63-75 (2008) (with S. Grudsky). - On
the level sets of the resolvent norm of a linear
operator,
*Bulletin LMS,*40, 3, 493-504 (2008). - Bernoulli free-boundary problems,
*Memoirs AMS,*196, 914, 70 pp. (2008) (with J.F. Toland). - On
the definition of pseudospectra,
*Bulletin LMS,*41, 3, 524-534 (2009). - The level sets of the resolvent norm and convexity properties of Banach spaces,
*Archiv der Mathematik,*93, 1, 59-66 (2009) (with S. Shkarin). - Toeplitz matrices with variable coefficients, pseudodifferential operators, and
Strichartz's method,
*Math. Nachr.*283, 1, 126-138 (2010). - Pseudospectra
of semigroup generators,
*Bulletin LMS,*42, 6, 1031-1034 (2010). - On some open problems in spectral theory,
*Operator Theory and Its Applications. In Memory of V. B. Lidskii (1924-2008). Amer. Math. Soc. Transl.*231, 173-180 (2010). - Applications of Blaschke products to the spectral theory of Toeplitz operators, In:
*J. Mashreghi and E. Fricain, Blaschke Products and Their Applications. Fields Institute Communications,*1-30 (2012) (with S. Grudsky). - An estimate for the Morse index of a Stokes wave,
*Arch. Rational Mech. Anal.*209, 1, 41-59 (2013). - On the limit behaviour of second order relative spectra of self-adjoint operators,
*Journal of Spectral Theory,*3, 4, 535-552 (2013). - On
negative eigenvalues of two-dimensional Schroedinger operators,
*Proceedings LMS,*108, 2, 441-483 (2014). - On the Amick-Fraenkel
conjecture,
*Quarterly J. Math.*65, 1, 267-278 (2014). - Extension of the unit normal vector field from a hypersurface,
*Georgian Math. J.*22, 3, 355-359 (2015) (with R. Duduchava and G. Tephnadze). - Level sets of the resolvent norm of a linear operator revisited,
*Mathematika,*62, 1, 243-265 (2016) (with E.B. Davies). - Quantitative results on continuity of the spectral factorization mapping in the scalar case,
*Boletín de la Sociedad Matemática Mexicana,*22(2), 517-527 (2016) (with L. Ephremidze and I. Spitkovsky).