The Complex and Hypercomplex Analysis group was founded in 1999 and focuses it research on applications and higher dimensional generalisations of complex analysis with the main focus on Hypercomplex analysis. It has a wide range of international collaboration, which includes other leading research centers in Hypercomplex Analysis, like the groups at Ghent University, Politecnico di Milano, University of Science and Technology of China, TU Bergakademie Freiberg, University of Wuhan, University of Macau, Bauhaus Universitaet Weimar, and the Center of Excellence in Hypercomplex Analysis at Chapman University (U.S.A.).
Essential part of its activities is an annual intensive course, which counted in the past with lecturers like D. Alpay, R. Aron, H. Feichtinger, M. Fornasier, R. Novikov, L. Paivarinta, M. Ruzhansky, S. Siltanen, F. Sommen, and J. Wirth, among many others. This is complemented with an annual workshop were both leading experts and young reseachers present their ideas. These acivities allow for an continuous influx of new ideas which is also being used by many PhD students from all over the world to discuss and evaluate their ideas.
Current research topics are
- Fractional Clifford analysis and corresponding potential theory - Study of discrete structures in the context of Clifford algebras (including analytic, geometric, and combinatorial properties) - Riemann Hilbert problems for matrix orthogonal polynomials and Painlevé equations and differential properties as well as over non-commutative structures - Approximation theory (polynomials, splines, wavelets, Gabor systems, curvelets, shearlets) In the context of hypercomplex analysis - Spectral theory for quaternionic normal operators - Pseudodifferential calculus for operators defined on the spin group - Harmonic and Gabor analysis in hyperbolic spaces - Reproducing kernel Hilbert and Krein modules - Generalised Clifford algebras and Dirac operators with SU(n)-symmetries
email: ukaehler@ua.pt