Analysis: Partial Differential and Integral Equations, Spectral Theory, Functional Analysis, Complex Variables,
Microlocal Analysis, Global Analysis
Applications: Fluid Dynamics, Elasticity Theory
Recent Publications
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 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).