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supported by the National Basic Research Program of China (Grant No. 1999075105);the National Natural Science Foundation of China (Grant No. 10471002);Research Foundation for Doctoral Programm (Grant No. 20050574002)
The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.
Research supported by the NNSF (19631080);973 Project of China (1999075105);NSF of Guangdong (030497,020586);NSF of Guangzhou (232)
The three-line theorem on the octonions is obtained, which generalizes the result of J. Peetre and P. Sj?lin from the associative Clifford algebra to non-associative octonion algebra.