2015/11/18 by Niraj K. Shukla, Shukla, Niraj K., Saurabh Chandra Maury +3
Computer Science · Mathematics · #11S85 #42C15 #42C40 #43A70 #Advanced Data Compression Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1511.05703
openalex publication_date 2015/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we establish theory of semi-orthogonal Parseval wavelets associated to generalized multiresolution analysis (GMRA) for the local field of positive characteristics (LFPC). By employing the properties of translation invariant spaces on the core space of GMRA we obtain a characterization of semi-orthogonal Parseval wavelets in terms of consistency equation for LFPC. As a consequence, we obtain a characterization of an orthonormal (multi)wavelet to be associated with an MRA in terms of multiplicity function as well as dimension function of a (multi)wavelet. Further, we provide characterizations of Parseval scaling functions, scaling sets and bandlimited wavelets together with a Shannon type multiwavelet for LFPC.