FAST ALGORITHMS FOR CALDERON-ZYGMUND SINGULAR INTEGRAL-OPERATORS

Many people would say that Calderon-Zygmund operators have almost diag onal matrices in orthonormal wavelet bases. We will show that this sta tement is not true as stated. In contrast, the ''non-standard matrix r epresentation'' of Calderon-Zygmund operators always yields almost dia gonal matrices. The Beyklin-Coifman-Rokhlin fast algorithm amounts to replacing these almost diagonal matrices by banded ones. We compute th e operator norm of the error term in this approximation and give sharp estimates. (C) 1996 Academic Press, Inc.