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Vector-valued nonuniform multiresolution analysis on local fields.
- Source :
-
International Journal of Wavelets, Multiresolution & Information Processing . Jul2015, Vol. 13 Issue 4, p-1. 22p. - Publication Year :
- 2015
-
Abstract
- A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V0 of L2(K, ℂM) has an orthonormal basis of the form {Φ (x - λ)}λ∈Λ where Λ = {0, r/N} + 풵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 풵 = {u(n) : n ∈ ℕ0}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02196913
- Volume :
- 13
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- International Journal of Wavelets, Multiresolution & Information Processing
- Publication Type :
- Academic Journal
- Accession number :
- 108564246
- Full Text :
- https://doi.org/10.1142/S0219691315500290