My research began with this project which was initiated by paper [4]. I solved a conjecture related to the algebra of box spline space in [4] by introducing a concept of sadditivity and proving the equivalency between the conjecture and sadditivity. I learned how to conduct research in progress with this project by collaborating with Amos, Carl, RongQing, and Sherm whom I regard as mentors of mine. They developed my research capability and inspired me to become a mathematician. I enjoyed my wonderful years as a Ph.D. student at the University of Alberta and a Research Associate at UWMadison.

 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), 223242. 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), 209250. PDF
 Rong Qing Jia, Sherman D. Riemenschneider, Zuowei Shen, Dimension of kernels of linear operators, American Journal of Mathematics 114(1992), 157184. PDF
 Zuowei Shen, Dimension of certain kernel spaces of linear operators, Proceedings of the American Mathematical Society 112(1991), 381390. PDF
Interpolaitions by Box Spliens
Hermite interpolation on the lattice was first introduced in [2]. Compactly supported fundamental solutions (Lagrange functions) for cardinal interpolations and Hermite interpolations were constructed in [1] using box splines. Approximation of fitting a curve, surface or function to scattered, possibly noisy, data can be found here.

 S. D. Riemenschneider, Zuowei Shen, Interpolation on the lattice hZ^{s}: Compactly supported fundamental solutions, Numerische Mathematik, 70(1995), 331351. PDF
 K. Jetter, S.D. Riemenschneider, Zuowei Shen, Hermite interpolation on the lattice Z^{d}, SIAM Journal on Mathematical Analysis 25(1994), 962975. PDF