A sampling theory for non-decaying signals in mixed Lebesgue spaces. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Han, Yang; Liu, Bei; Zhang, Qingyue
• Is Part Of: Applicable analysis. Volume 101:Issue 1(2022)
• Page Start: 173
• Page End: 191
• Publication Date: 2022-01-02
• Subjects: Zuhair Nashed; Mixed Lebesgue spaces -- shift-invariant spaces -- sampling theory -- non-decaying signals -- submultiplicative weights; 94A20 -- 42C15 -- 42C40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1736286
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we study the sampling theory for non-decaying signals in mixed Lebesgue spaces L p, q ( R d + 1 ) . First, we give some Riesz-type bounds, which connect the weighted discrete norms of the samples to the weighted continuous norms of original and interpolated signals. Then, we prove that the sampling and reconstruction through the Riesz-type bounds are stable when the generated kernel is in the appropriate mixed Wiener amalgam spaces.