{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:08:05Z","timestamp":1753880885596,"version":"3.41.2"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p> In recent years, the concepts of frame in [Formula: see text]-Hilbert space and [Formula: see text]-frames in [Formula: see text]-Hilbert space have been introduced. The [Formula: see text]-frames in the [Formula: see text]-Hilbert space are more generalized than the ordinary frames. This paper deals with the problem of sum of [Formula: see text]-frames in [Formula: see text]-Hilbert space. First, the sufficient condition for the finite sum of [Formula: see text]-frames and Bessel sequences in [Formula: see text]-Hilbert space is given. Then, some results on the operator [Formula: see text] and pre-frame operator are given, and some new results on the sum of [Formula: see text]-frame are proved. We then discuss several results for the perturbation and stability of the [Formula: see text]-frames in [Formula: see text]-Hilbert space about the sum of the [Formula: see text]-frames. <\/jats:p>","DOI":"10.1142\/s0219691323500352","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T13:55:13Z","timestamp":1689083713000},"source":"Crossref","is-referenced-by-count":0,"title":["A study on the sum of K-frames in n-Hilbert space"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7424-0600","authenticated-orcid":false,"given":"Gang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2023,8,1]]},"reference":[{"issue":"2","key":"S0219691323500352BIB001","first-page":"123","volume":"1","author":"Akbar A. A.","year":"2013","journal-title":"Iran. J. Math. Sci. 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