ANALYSIS AND APPROXIMATION THEORY SEMINAR UNIVERSITY OF ALBERTA Construction of compactly supported biorthogonal wavelets in L 2 (IR s

: This paper presents a general construction of compactly supported biorthogonal wavelets in L 2 (IR s ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets of increasing smoothness is provided. Several examples are computed. The estimate of smoothness of those examples are given based on criteria established in [RiS3]. AMS Subject Classification: Primary 45A05, 65D05, 65D15, 26B05 Secondary 41A15, 41A63 Keywords: multivariate biorthogonal wavelets, multivariate wavelets, box splines, matrix extension y Research supported in part by NSERC Canada under Grant # A7687 1 1. Introduction The present paper is the fourth of our series of papers on the construction of multivariate wavelets by using box splines. In the first paper [RiS1], we constructed exponentially decaying orthogonal wavelets from box splines for the case s = 2; 3. In [RiS2], we constructed compactly supported pre-wavelets from box splines for the case s = 1; 2; ..