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An analysis method for sampling in shift-invariant spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-7620-9386
2005 (English)In: International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, E-ISSN 1793-690X, Vol. 3, no 3, 301-319 p.Article in journal (Refereed) Published
Abstract [en]

A subspace V of L2(ℝ) is called shift-invariant if it is the closed linear span of integer-shifted copies of a single function.As a complement to classical analysis techniques for sampling in such spaces, we propose a method which is based on a simple interpolation estimate of a certain coefficient mapping. Then we use this method to derive both new results and relatively simple proofs of some previously known results. Among these are some results of rather general nature and some more specialized results for B-spline wavelets. The main problem under study is to find a shift x0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f(x0 + k + δk))k∈ℤ, either when all δk = 0 or in the irregular sampling case with an upper bound supk|δk| < δ.

Place, publisher, year, edition, pages
2005. Vol. 3, no 3, 301-319 p.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-10604DOI: 10.1142/S0219691305000877Local ID: 96e28120-ba9d-11db-b560-000ea68e967bOAI: oai:DiVA.org:ltu-10604DiVA: diva2:983549
Note
Validerad; 2005; 20070115 (grip)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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