Applied harmonic analysis and partial differential equations

Project Details


A central problem in mathematics is the analysis of functions. Functional analysis is the branch of mathematics in which spaces of functions are studied on an abstract level. This project aims to pursue further developments in two active research areas in functional analysis, namely, applied harmonic analysis and the theory of partial differential equations.

One of the main themes of applied harmonic analysis is the development and study of representation systems of functions intended for concrete applications, e.g., in image, audio, and data processing. Such systems consist of a collection of “nice” basis functions (building blocks) such that all functions -belonging to some a priori fixed space- may be efficiently decomposed into these basis functions. We study several questions about representation systems, some of which arise from their use in image processing.

Partial differential equations are ubiquitous in sciences as many real-world phenomena may be mathematically modeled using them. We consider various questions concerning the behavior of solutions of partial differential equations and apply them to study inverse problems.
Effective start/end date1/09/2331/08/27


  • Higher order shearlet systems
  • Sparse approximation
  • Coorbit spaces
  • Approximation results for zero solutions of partial differential equations
  • The problem of parameter dependence for solutions of partial differential equations
  • Linear topological invariants

Flemish discipline codes

  • Functional analysis
  • Harmonic analysis on Euclidean spaces
  • Image processing
  • Partial differential equations


Explore the research topics touched on by this project. These labels are generated based on the underlying awards/grants. Together they form a unique fingerprint.