Abstract
For any ϕ(t) in L2(ℝ), let V(ϕ) be the closed shift invariant subspace of L2(ℝ) spanned by integer translates {ϕ(t - n) : n ∈ ℤ} of ϕ(t). Assuming that ϕ(t) is a frame or a Riesz generator of V(ϕ), we first find conditions under which V(ϕ) becomes a reproducing kernel Hilbert space. We then find necessary and sufficient conditions under which an irregular or a regular shifted sampling expansion formula holds on V(ϕ) and obtain truncation error estimates of the sampling series. We also find a sufficient condition for a function in L2(ℝ) that belongs to a sampling subspace of L2(ℝ). Several illustrating examples are also provided.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Wavelets, Multiresolution and Information Processing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
