Continuous wavelet transform on local fields

Abstract

abstract:The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of its basic properties. Its inversion formula, the Parseval relation and associated convolution are also studied.

A Characterization of Orthonormal Multilevel Wavelet Families in Sobolev Space over Local Fields of Positive Characteristic

“…The space S ′ (K) of continuous linear functional on S (K) (the space of all finite linear combinations of characteristics functions of ball of K) is called the space of distributions. The Fourier transform of f ∈ S (K) is denoted byf (ξ) and defined by thê 1) and the inverse Fourier transform by…”