Amos Ron

Professor of Computer Sciences and Mathematics and member of the Center for Mathematical Sciences

Computer Sciences Department
University of Wisconsin
1210 W. Dayton St.
Madison, WI 53706-1685

telephone: (608) 262-1204
fax: (608) 262-9777
Ph.D., Tel Aviv University, 1987
Interests: Multivariate splines, wavelets, radial basis function approximation, polynomial interpolation, windowed Fourier transform, approximation to scattered data

Research Summary

A spline space is a collection of `good' functions that you want to consider for approximating others, and which satisfies certain properties, such as being piecewise-polynomials/piecewise-exponentials, being spanned by compactly supported functions, or easily computable. At present I am interested in the model where the space of approximants is a linear space of functions of several variables and is assumed to be invariant under integer translations. My most recent work is concerned with the application of this model in the context of:

(1) Constructions of wavelet systems tailored for specific applications (such as data compression or feature detection).

(2) Useful methods for approximating scattered data in several dimensions.

Sample Recent Publications

Compactly supported tight affine spline frames in L2(Rd) (with Z. Shen), Mathematics of Computation, 1998.

Approximation orders of FSI spaces in L2(Rd) (with C. de Boor and R. DeVore), Constructive Approximation, 1998.

Tight compactly supported wavelet frames of arbitrarily high smoothness (with K. Gröchenig), Proceedings of the American Mathematical Society, 1998.

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