Pencho Petrushev

Scientific interests

General:

Approximation Theory, Harmonic Analysis, Numerical Analysis

Specific:

1. Spaces of distributions such as Hardy, Besov and Triebel-Lizorkin spaces in harmonic, nonclassical, anisotropic and geometric settings
2. Construction of bases and frames (needlets) for Besov and Triebel- Lizorkin spaces in nonclassical and geometric settings
3. Nonlinear approximation from rational functions, splines, frames, ridge functions and more general dictionaries
4. Nonlinear n-term approximation of harmonic functions from linear combinations of shifts of the fundamental solution of the Laplace equation (Newtonian kernel)
5. Application of spherical needlets to approximation and fast evaluation of quantities represented in high degree surface or solid spherical harmonics
6. Reproduction of sound from optical sound tracks of digital scans of motion picture films