A new class of plurisubharmonic functions on the octonionic plane double-struck O sign 2≃ℝ 16 is introduced. An octonionic version of theorems of A.D. Aleksandrov (Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 13(1):5-24, 1958) and Chern-Levine-Nirenberg (Global Analysis, pp. 119-139, 1969), and Błocki (Proc. Am. Math. Soc. 128(12):3595-3599, 2000) are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of double-struck O sign 2≃ℝ 16. In particular, a new example of Spin(9)-invariant valuation on ℝ 16 is given.
- Convex sets
- Plurisubharmonic functions