Amos Ron's Research Interests

Amos Ron's Research Interests

abstracts at ftp

Approximation to scattered data, using translates of one basis function such as the Gaussian kernel, the thin plate spline, or the multiquadric.

Multivariate polynomial interpolation; specifically, the least solution for that problem.

Wavelet systems and Gabor systems: primarily fiberization techniques for such sets (useful for the study of the Riesz basis property, and the frame property of such systems).

Shift-invariant spaces. These are spaces of functions that are invariant under integer translations. I am interested in several topics in this area including the approximation orders and approximation schemes from such spaces, and shift-invariant bases for such spaces. More specific topics here include box splines , and refinable spaces (that are used for wavelet constructions).

Dimension formulae for joint kernels of commuting linear operators. This is a topic that started at box spline theory, and has connections to ideal theory and matroids.