Local Average Sampling and Reconstruction with Fundamental Splines of Fractional Order. (27th July 2019)

• Record Type: Journal Article
• Authors: Devaraj, P.; Massopust, Peter; Yugesh, S.
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 10(2019)
• Page Start: 1215
• Page End: 1229
• Publication Date: 2019-07-27
• Subjects: Average sampling -- fractional spline -- fractional spline interpolation -- fundamental cardinal spline; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1604544
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We analyze sampling and average sampling techniques for fractional spline subspaces of L 2 ( R ) . Fractional B-splines β σ are extensions of Schoenberg's polynomial splines of integral order to real order σ > − 1 . We present the interpolation with fundamental splines of fractional order for σ ≥ 1 and the average sampling with fundamental splines of fractional order for σ ≥ 3 2 . Further, we generalize Kramer's lemma in the context of local average sampling.