低维空间下的短支集样条小波基

B.~Han and Z.~Shen constructed afamily of univariate short support Riesz waveletsfrom uniform B-splines in 2006. A bivariate spline Riesz wavelet basis fromthe Loop scheme was derived by B.~Han and Z.~Shen in 2005.Motivated bythese two papers, we develop in this article ageneral theory and a construction method to derive small supportRiesz wavelets in low dimensions from refinable functions. Inparticular, we obtain small support spline Riesz wavelets frombivariate and trivariate box splines. Small support Riesz waveletsare desirable for developing efficient algorithms in variousapplications. For example, the short support Riesz wavelets constructed byB.~Han and Z.~Shen were used in a surface fitting algorithm byM.J.~Johnson, Z.~Shen and Y.H.~Xu in 2009, and the Riesz wavelet basis from the Loop scheme wasused in a very efficient geometric mesh compression algorithm byA. Khodakovsky, P. Schr"oder and W. Sweldens in 2000.