Year: 2026
Type: article
Abstract: We introduce a slice-based quaternionic analog of wavelet sets in the right- quaternionic Hilbert space L 2 ( R d , H ) $L^{2}(\mathbb {R}^{d},\mathbb {H})$ upper L squared left parenthesis double struck upper R Superscript d Baseline comma double struck upper H right parenthesis . Using a slice-quaternionic Fourier transform, we characterize boundedness and Parseval tightness of affine systems generated by ψ ^ = ( 2 π ) − d / 2 χ E q $\widehat {\psi }=(2\pi )^{-d/2}\chi _{E}q$ ModifyingAbove psi With caret equals left parenthesis 2 pi right parenthesis Superscript negative d divided by 2 Baseline chi Subscript upper E Baseline q via translation and dilation multiplicity conditions on E . These results extend the classical frame wavelet-set theory of Dai et al. (2003, J. Comput. Appl. Math. 155, 69–82) to the quaternionic setting under a natural slice-phase restriction. Several dyadic, directional, and multiwavelet examples illustrate the framework and provide the first systematic construction of quaternionic wavelet sets.
Source: Canadian Mathematical Bulletin
Institutions: University of Delhi, Sultan Qaboos University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7165023055
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