{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:27:31Z","timestamp":1762432051315,"version":"3.41.2"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:p> The Franklin wavelet is constructed using the multiresolution analysis (MRA) generated from a scaling function [Formula: see text] that is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text] for every [Formula: see text]. For [Formula: see text] and [Formula: see text], it is shown that if a function [Formula: see text] is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text], for [Formula: see text], and generates MRA with dilation factor [Formula: see text], then [Formula: see text]. Conversely, for [Formula: see text], it is shown that there exists a [Formula: see text], as satisfying the above conditions, that generates MRA with dilation factor [Formula: see text]. The frame MRA (FMRA) is useful in signal processing, since the perfect reconstruction filter banks associated with FMRA can be narrow-band. So it is natural to ask, whether the above results can be extended for the case of FMRA. In this paper, for [Formula: see text], we prove that if [Formula: see text] generates FMRA with dilation factor [Formula: see text], then [Formula: see text]. For [Formula: see text], we prove similar results when [Formula: see text]. In addition, for [Formula: see text] we prove that there exists a function [Formula: see text] as satisfying the above conditions, that generates FMRA. Also, we construct tight wavelet frame and wavelet frame for such scaling functions. <\/jats:p>","DOI":"10.1142\/s0219691321500326","type":"journal-article","created":{"date-parts":[[2021,7,11]],"date-time":"2021-07-11T12:36:45Z","timestamp":1626007005000},"source":"Crossref","is-referenced-by-count":3,"title":["Frame multiresolution analysis of continuous piecewise linear functions"],"prefix":"10.1142","volume":"19","author":[{"given":"S. Pitchai","family":"Murugan","sequence":"first","affiliation":[{"name":"Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600 005, India"}]},{"given":"G. 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