Structured function systems are sequences of distinguished elements of a complete function space that can serve as coordinate components (orthogonal bases, Riesz bases, frames) for more elusive functions. Besides orthogonal bases of harmonics, polynomials or almost periodic functions, wavelets of many sorts and frames of entire functions have reached an impressive array of applications (in signal processing, image reconstruction, remote sensing) and also have marked some purely theoretical topics (singular integrals, spectral analysis).
In spite of the maturity of the subject and notable recent advances there are many clear-cut mathematical questions about such structured function systems. It is the aim of the workshop to address two directions of such mathematical challenges, in front of a mixed audience, consisting of experts in several apparently disconnected areas.
This ESI workshop will build up on recently discovered links between Gabor and wavelet analysis on the one hand and real algebraic geometry, complex analysis, system theory, special functions, and approximation theory on the other hand. We intend to isolate a few theoretical questions which should intrigue and attract the ”pure” participants. Whereas it is not unexpected that complex analysis plays a role in such investigations, it is quite surprising that Tarski’s elimination of quantifiers or Potapov-Blaschke factorization should be on the working bench of frame experts.
The workshop will bring together experts in wavelet theory and real algebraic geometry on the one hand, and experts in Gabor frames and complex analysis and special functionis on the other hand.