A computer algebra approach to orthonormal wavelets Fr´ ed´ eric Chyzak Frederic.Chyzak@inria.fr INRIA Rocquencourt, F–78153 Le Chesnay, France Peter Paule Peter.Paule@risc.uni-linz.ac.at Research Institute for Symbolic Computation Johannes Kepler University, A–4040 Linz, Austria Otmar Scherzer scherzer@rz.mathematik.uni-muenchen.de Institut f¨ ur Angewandte Mathematik LMU–M¨ unchen, D–80333 M¨ unchen, Germany On leave from Industrial Mathematics Institute, Linz, Austria Armin Schoisswohl schoisswohl@indmath.uni-linz.ac.at Industrial Mathematics Institute Johannes Kepler University, A–4040 Linz, Austria Burkhard Zimmermann Burkhard.Zimmermann@risc.uni-linz.ac.at Research Institute for Symbolic Computation Johannes Kepler University, A–4040 Linz, Austria February 16, 2000 1 Introduction This paper is based on [CPSSZ00] which is to appear in Experimental Mathe- matics. The name wavelet was made up by French researchers [MAFG82, Mor83, GM84] for a particular class of functions. The existence of wavelet-like functions has been known since the beginning of the century (a notable example is what is known as the Haar wavelet today [Haa10]). However, only recently the unify- ing concepts necessary for a general understanding of wavelets were provided 1