BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sergei Plaksa (National Academy of Sciences of Ukraine) DTSTART:20230709T154500Z DTEND:20230709T170000Z DTSTAMP:20260409T220750Z UID:HCS2023/1 DESCRIPTION:Title: Monogenic functions in infinite-dimensional vector spaces with a commutati ve multiplication and harmonic vectors\nby Sergei Plaksa (National Aca demy of Sciences of Ukraine) as part of Hypercomplex Seminar 2023\n\n\nAbs tract\nWe consider special topological vector spaces with a commutative mu ltiplication for some\nof elements of the spaces. The consideration of suc h topological vector spaces is motivated by the\nneed to describe all spat ial harmonic functions as components of hypercomplex monogenic functions.\ nMonogenic functions are understood as continuous and differentiable in th e sense of Gâteaux functions.\nWe prove that all spatial harmonic functio ns are components of monogenic functions taking values in\nthe mentioned s paces. We describe relations between the mentioned monogenic functions and harmonic\nvectors in the three-dimensional real space and establish suffi cient conditions for infinite monogeneity of functions. Unlike the classic al complex analysis\, it is done in the case where the validity of the Cau chy integral formula for monogenic functions remains an open problem.\n LOCATION:https://researchseminars.org/talk/HCS2023/1/ END:VEVENT END:VCALENDAR