My research began with a project initiated by , in which I solved a conjecture of Dahmen and Michelli related to the algebra of the box spline space. I introduced the concept of s-additivity and proved its equivalence to the conjecture. Working with Amos, Carl, Rong-Qing, and Sherm on this project helped me learn how to conduct research and develop my research capabilities, inspiring me to pursue a career as a mathematician. I enjoyed several memorable years as a student at the University of Alberta and as a Research Associate at UW-Madison.
- Carl de Boor, Amos Ron, Zuowei Shen, On ascertaining inductively the dimension of the joint kernel of certain commuting linear operators II, Advances in Mathematics, 123 (1996), 223-242. PDF
- Carl de Boor, Amos Ron, Zuowei Shen, On ascertaining inductively the dimension of the joint kernel of certain commuting linear operators, Advances in Applied Mathematics, 17(1996), 209-250. PDF
- Rong Qing Jia, Sherman D. Riemenschneider, Zuowei Shen, Dimension of kernels of linear operators, American Journal of Mathematics 114(1992), 157-184. PDF
- Zuowei Shen, Dimension of certain kernel spaces of linear operators, Proceedings of the American Mathematical Society 112(1991), 381-390. PDF
Interpolaitions by Box Spliens
Hermite interpolation on the lattice was first introduced in . Compact fundamental solutions (Lagrange functions) for cardinal interpolations and Hermite interpolations were constructed in  using box splines. The approximation of fitting a curve, surface, or function to scattered, possibly noisy, data can be found here.