Harmonic Analysis

Classical harmonic analysis studies functions and differential- and integral operators on Euclidean spaces by using Fourier series and Fourier integrals. Modern harmonic analysis is a very active and broad research area, which for example includes analysis on groups more general than the Euclidean space, and analysis of spaces of functions where the trigonometric functions have been replaced by for example eigenfunctions, wavelets or wave packets. At the Department of Mathematical Sciences, we conduct research on and apply harmonic analysis in areas such as:

• Dynamical systems, ergodic theory, combinatorics and number theory.
• Singular integral operators and wavelets.
• Holomorphic functional calculus of non-selfadjoint differential operators.
• Index theory for differential operators.
• Spectral theory and eigenvalue estimates for Schrödinger operators and Laplace-Beltrami operators.
• Geometric and microlocal analysis on Riemannian manifolds.
• Orthogonal polynomials and special functions related to Lie groups and quantum groups.
• Representations of Lie groups and analysis on symmetric and homogeneous spaces.
• Convexity of energy functions on Teichmüller space.