{"scopus_import":"1","quality_controlled":"1","abstract":[{"text":"A tight frame is the orthogonal projection of some orthonormal basis of Rn onto Rk. We show that a set of vectors is a tight frame if and only if the set of all cross products of these vectors is a tight frame. We reformulate a range of problems on the volume of projections (or sections) of regular polytopes in terms of tight frames and write a first-order necessary condition for local extrema of these problems. As applications, we prove new results for the problem of maximization of the volume of zonotopes.","lang":"eng"}],"author":[{"last_name":"Ivanov","full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","first_name":"Grigory"}],"intvolume":"        64","citation":{"ista":"Ivanov G. 2021. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 64(4), 942–963.","ama":"Ivanov G. Tight frames and related geometric problems. <i>Canadian Mathematical Bulletin</i>. 2021;64(4):942-963. doi:<a href=\"https://doi.org/10.4153/s000843952000096x\">10.4153/s000843952000096x</a>","short":"G. Ivanov, Canadian Mathematical Bulletin 64 (2021) 942–963.","chicago":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” <i>Canadian Mathematical Bulletin</i>. Canadian Mathematical Society, 2021. <a href=\"https://doi.org/10.4153/s000843952000096x\">https://doi.org/10.4153/s000843952000096x</a>.","mla":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” <i>Canadian Mathematical Bulletin</i>, vol. 64, no. 4, Canadian Mathematical Society, 2021, pp. 942–63, doi:<a href=\"https://doi.org/10.4153/s000843952000096x\">10.4153/s000843952000096x</a>.","apa":"Ivanov, G. (2021). Tight frames and related geometric problems. <i>Canadian Mathematical Bulletin</i>. Canadian Mathematical Society. <a href=\"https://doi.org/10.4153/s000843952000096x\">https://doi.org/10.4153/s000843952000096x</a>","ieee":"G. Ivanov, “Tight frames and related geometric problems,” <i>Canadian Mathematical Bulletin</i>, vol. 64, no. 4. Canadian Mathematical Society, pp. 942–963, 2021."},"isi":1,"department":[{"_id":"UlWa"}],"title":"Tight frames and related geometric problems","status":"public","month":"12","type":"journal_article","publication_identifier":{"eissn":["1496-4287"],"issn":["0008-4395"]},"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_type":"original","date_created":"2022-03-18T09:55:59Z","oa_version":"Preprint","date_published":"2021-12-18T00:00:00Z","keyword":["General Mathematics","Tight frame","Grassmannian","zonotope"],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.10055"}],"date_updated":"2023-09-05T12:43:09Z","_id":"10860","publication":"Canadian Mathematical Bulletin","issue":"4","doi":"10.4153/s000843952000096x","page":"942-963","acknowledgement":"The author was supported by the Swiss National Science Foundation grant 200021_179133. The author acknowledges the financial support from the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no. 075-15-2019-1926.","publication_status":"published","external_id":{"isi":["000730165300021"],"arxiv":["1804.10055"]},"year":"2021","publisher":"Canadian Mathematical Society","volume":64,"day":"18","oa":1,"language":[{"iso":"eng"}]}