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Process."],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:p> Due to [Formula: see text] not being a group under addition, [Formula: see text] admits no traditional wavelet or Gabor frame. This paper addresses a class of dilation-and-modulation ([Formula: see text]) Parseval frames for [Formula: see text]. We present a parametric expression of all [Formula: see text]-Parseval frames (frame sequences) and [Formula: see text]-orthonormal bases (systems); and develop an approach to obtain all [Formula: see text]-Parseval frames (frame sequences) and [Formula: see text]-orthonormal bases (systems) starting with one [Formula: see text]-Parseval frame for [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219691322500369","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T12:12:53Z","timestamp":1660133573000},"source":"Crossref","is-referenced-by-count":0,"title":["Dilation-and-modulation Parseval frames in the half space"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1699-050X","authenticated-orcid":false,"given":"Yun-Zhang","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, P. R. 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