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Biaxial monogenic functions from Funk‐Hecke's formula combined with Fueter's theorem
Author(s) -
Peña Peña Dixan,
Sommen Frank
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400209
Subject(s) - mathematics , holomorphic function , funk , invariant (physics) , pure mathematics , mathematical analysis , mathematical physics , physics , acoustics
Funk‐Hecke's formula allows a passage from plane waves to radially invariant functions. It may be adapted to transform axial monogenics into biaxial monogenics that are monogenic functions invariant under the product group SO( p )× SO( q ). Fueter's theorem transforms holomorphic functions in the plane into axial monogenics, so that by combining both results, we obtain a method to construct biaxial monogenics from holomorphic functions.