ON THE p - ADIC SPECTRAL ANALYSIS AND MULTIWAVELET ON L 2 ( Q np )

To Dong-Sik Kim on his 62nd birthday We try to generalize an explicit construction for an orthonormal system of eigen-functions of the Vladimirov operator on L 2 (Q n p) which was originally given by Vladimirov (1988). Also the multiwavelet analysis can be considered as the p-adic spectral analysis in L 2 (Q n p), using in part the recent work of Kozyrev (2002). denote the ring of integers, the field of complex numbers, the field of p-adic rational numbers, and the completion of the algebraic closure of Q p , respectively. Let ord p denote the unique p-adic ordinal over Q p such that ord p (p) = 1. The corresponding non-Archimedian absolute value is |x| p = p − ordp (x) .