- Ergodic theory with emphasis on connections with number theory, functional equations,and complex function theory.
- Banach spaces and Banach algebras, especially those consisting of continuous functions.
- Infinite matrices as operators on classical sequence spaces.
- Non-linear functional analysis with applications to differential equations.
- Approximation theory, Fourier analysis, wavelets, and differential equations, with emphasis on applications in inverse problems and tomography.
- Analysis and differential equations on groups and fractals.
- Infinite-Dimensional Analysis