Some relations between linear mappings and conjugations in idempotent analysis (Q1407371)

The author proves a large number of results showing that the theory of {lower semicontinuous dioid-valued linear mappings} in [\textit{V. N. Kolokoltsov} and \textit{V. P. Maslov}, ``Idempotent analysis and its applications'', Appendix by Pierre Del Moral, transl. from the Russian by V. E. Nazaikinskij, Dordrecht (1997; Zbl 0941.93001)] is closely related to the {theory of the abstract Fenchel-Moreau conjugations for functions with values in extensions of completely ordered groups} studied by \textit{J.-E. Martínez-Legaz} and \textit{I. Singer} [{Optimization} {21}, No. 4, 481--508 (1990; Zbl 0728.90071); ibid. {22}, No. 4, 483--511 (1991; Zbl 0728.06007); ibid. {30}, No. 4, 295--315 (1994; Zbl 0815.49026); {Positivity} {1}, No. 3, 193--218 (1997; Zbl 0899.49016), etc.].