Construction of frames for shift-invariant spaces

2011/09/15 by Pilipovic, Stevan, Simic, Suzana
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1109.3285

Abstract

We construct a sequence ϕ_i(⋅-j)| j∈\ZZ, i=1,...,r which constitutes a p-frame for the weighted shift-invariant space [V^p_μ(Φ)=∑_i=1^r∑_j∈ℤc_i(j)ϕ_i(⋅-j) | c_i(j)_j∈ℤ∈ℓ^p_μ, i=1,...,r, p∈[1,∞],] and generates a closed shift-invariant subspace of L^p_μ(ℝ). The first construction is obtained by choosing functions ϕ_i, i=1,...,r, with compactly supported Fourier transforms ϕ_i, i=1,...,r. The second construction, with compactly supported ϕ_i,i=1,...,r, gives the Riesz basis.

Related

• Frames for weighted shift-invariant spaces
• Frames and Oversampling Formulas for Band Limited Functions
• Linear combinations of frame generators in systems of translates
• Shift-invariant subspaces of Sobolev type
• Frames of translates with prescribed fine structure in shift invariant\n spaces