Multiresolution analysis on local fields and characterization of scaling functions
-
Biswaranjan Behera
and
Qaiser Jahan
Abstract.
The concepts of multiresolution analysis (MRA) and wavelet can be generalized to a local field 
of positive characteristic by using a prime element of such a field. An MRA is a sequence of closed subspaces of 
satisfying certain properties. We show that it is enough to assume that the discrete translates of a single function in the core subspace of the MRA form a Riesz basis instead of an orthonormal basis and show how to construct an orthonormal basis from a Riesz basis. We also prove that the intersection triviality condition in the definition of MRA follows from the other conditions of an MRA. The union density condition also follows if we assume that the Fourier transform of the scaling function is continuous at 0. Finally we characterize the scaling functions associated with such an MRA.
© 2012 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle
- A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
- Combined Sundman–Darboux transformations and solutions of nonlinear ordinary differential equations of second order
- Multiresolution analysis on local fields and characterization of scaling functions
- Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions
- Small gaps Fourier series and generalized variations
- Central limit theorems for radial random walks on matrices for
Articles in the same Issue
- Masthead
- Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle
- A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
- Combined Sundman–Darboux transformations and solutions of nonlinear ordinary differential equations of second order
- Multiresolution analysis on local fields and characterization of scaling functions
- Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions
- Small gaps Fourier series and generalized variations
- Central limit theorems for radial random walks on matrices for
