Nonuniform Multiwavelet Sets and Multiscaling Sets. (1st February 2016)

• Record Type: Journal Article
• Authors: Mittal, Shiva; Shukla, Niraj K.; Atlouba, Nadya A. S.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 2(2016)
• Page Start: 253
• Page End: 276
• Publication Date: 2016-02-01
• Subjects: Generalized scaling sets -- multiscaling sets -- multiwavelets -- multiwavelet sets -- nonuniform multiresolution analysis (NUMRA) -- nonuniform multiresolution analysis with multiplicity D (NUMRA-D) -- spectral pairs; 42C40 -- 65T60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1110592
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we study the theory of nonuniform minimally supported frequency multiwavelets and nonuniform multiscaling sets. A characterization of nonuniform multiwavelet sets is obtained which generalizes a result of Yu and Gabardo. After introducing a notion of generalized nonuniform scaling set, we obtain a characterization of nonuniform multiscaling sets associated with nonuniform multiresolution analysis having finite multiplicity. In addition, we provide a geometric construction to find families of symmetric nonuniform multiwavelet sets.