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Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a two-parameter family whose<jats:inline-formula><jats:alternatives><jats:tex-math>${\\mathscr{H}}\\mathcal {C}^{2}$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>H<\/mml:mi><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-smoothness is guaranteed whenever the parameters are chosen from a certain polygonal region. The construction of this new family is inspired by the geometric insight into the ternary interpolatory scalar three-point subdivision scheme by Hassan and Dodgson. The smoothness of our new family of Hermite schemes is proven by means of joint spectral radius techniques.<\/jats:p>","DOI":"10.1007\/s10444-021-09854-x","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T13:02:43Z","timestamp":1616504563000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Joint spectral radius and ternary hermite subdivision"],"prefix":"10.1007","volume":"47","author":[{"given":"M.","family":"Charina","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6878-7784","authenticated-orcid":false,"given":"C.","family":"Conti","sequence":"additional","affiliation":[]},{"given":"T.","family":"Mejstrik","sequence":"additional","affiliation":[]},{"given":"J.-L.","family":"Merrien","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"key":"9854_CR1","doi-asserted-by":"crossref","unstructured":"Cabrelli, C.A., Heil, C., Molter, U.M.: Self-similarity and multiwavelets in higher dimensions. 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