Construction of Frames for Shift-Invariant Spaces
Copyright policy )Construction of Frames for Shift-Invariant Spaces
We construct a sequence{ϕi(·-j)∣j∈ℤ, i=1,…,r}which constitutes ap-frame for the weighted shift-invariant spaceVμp(Φ)={∑i=1r∑j∈ℤci(j)ϕi(·-j)∣{ci(j)}j∈ℤ∈ℓμp, i=1,…,r},p∈[1,∞], and generates a closed shift-invariant subspace ofLμp(ℝ). The first construction is obtained by choosing functionsϕi,i=1,…,r, with compactly supported Fourier transformsϕ^i,i=1,…,r. The second construction, with compactly supportedϕi,i=1,…,r,gives the Riesz basis.
Mathematics - Functional Analysis, \(p\)-frame, shift-invariant space, QA1-939, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, General harmonic expansions, frames, Mathematics, Riesz basis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA)
Mathematics - Functional Analysis, \(p\)-frame, shift-invariant space, QA1-939, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, General harmonic expansions, frames, Mathematics, Riesz basis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA)
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