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This theory is centred around the concept of \u03c8\u2010hyperholomorphic functions related to a so\u2010called structural set \u03c8 of or respectively. The main goal of this paper is to develop the nucleus of the \u2010hyperholomorphic function theory, i.e., simultaneous null solutions of two Cauchy\u2010Riemann operators associated to a pair of structural sets of . Following a matrix approach, a generalized Borel\u2010Pompeiu formula and the corresponding Plemelj\u2010Sokhotzki formulae are established.<\/jats:p>","DOI":"10.1002\/mana.201300072","type":"journal-article","created":{"date-parts":[[2015,4,14]],"date-time":"2015-04-14T18:46:04Z","timestamp":1429037164000},"page":"1451-1475","source":"Crossref","is-referenced-by-count":12,"title":["On some structural sets and a quaternionic \u2010hyperholomorphic function theory"],"prefix":"10.1002","volume":"288","author":[{"given":"Ricardo","family":"Abreu\u00a0Blaya","sequence":"first","affiliation":[{"name":"Facultad de Inform\u00e1tica y Matem\u00e1tica Universidad de Holgu\u00edn Holgu\u00edn 80100 Cuba"}]},{"given":"Juan","family":"Bory\u00a0Reyes","sequence":"additional","affiliation":[{"name":"ESIME\u2010Zacatenco Instituto Polit\u00e9cnico Nacional, M\u00e9xico DF 07738 M\u00e9xico"},{"name":"Departamento de Matem\u00e1tica Universidad de Oriente Santiago de Cuba 90500 Cuba"}]},{"given":"Al\u00ed","family":"Guzm\u00e1n\u00a0Ad\u00e1n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Universidad de Oriente Santiago de Cuba 90500 Cuba"}]},{"given":"Uwe","family":"Kaehler","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Universidade de Aveiro P\u20103810\u2010193 Aveiro Portugal"}]}],"member":"311","published-online":{"date-parts":[[2015,4,14]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.10.022"},{"key":"e_1_2_11_3_1","volume-title":"Clifford Analysis","author":"Brackx F.","year":"1982"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.4171\/ZAA\/1002"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01292723"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01199562"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7295-9"},{"key":"e_1_2_11_8_1","volume-title":"Quaternionic and Clifford Calculus for Physicists and Engineers","author":"G\u00fcrlebeck K.","year":"1997"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF03041935"},{"key":"e_1_2_11_10_1","unstructured":"V. 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