On the Legendre and Laplace transformations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 3-4, pp. 517-568. 
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     author = {H\"ormander, Lars},
     title = {On the {Legendre} and {Laplace} transformations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {517--568},
     publisher = {Scuola normale superiore},
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     number = {3-4},
     year = {1997},
     mrnumber = {1655531},
     zbl = {1016.44003},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1997_4_25_3-4_517_0/}
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Hörmander, Lars. On the Legendre and Laplace transformations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 3-4, pp. 517-568. http://www.numdam.org/item/ASNSP_1997_4_25_3-4_517_0/

[1] W. Fenchel, On conjugate convex functions, Canad. J. Math. 1 (1949), 73-77. | MR | Zbl

[2] W. Fenchel, Convex cones, sets and functions, Mimeographed lecture notes, Princeton University, 1953. | Zbl

[3] I.M. Gelfand - G. E. ŠILOV, Fourier transforms of rapidly increasing functions and the question on the uniqueness of Cauchy's problem, Uspehi Mat. Nauk 8 (1953), 3-54. | MR | Zbl

[4] I.M. Gelfand - G.E. Šilov, Generalized Functions III. Theory of Differential Equations, Academic Press, New York, London, 1967. Translated from the Russian 1958 edition and the German 1964 edition.

[5] L. Hörmander, La transformation de Legendre et le théorème de Paley-Wiener, C. R. Acad. Sci. Paris 240 (1955), 392-395. | MR | Zbl

[6] L. Hörmander, Notions of Convexity, Birkhäuser, 1994. | MR | Zbl

[7] B.J. Lewin, Nullstellenverteilung Ganzer Funktionen, Akademie-Verlag, Berlin, 1962. | MR | Zbl

[8] S. Mandelbrojt, Sur les fonctions convexes, C. R. Acad. Sci. Paris 209 (1939), 977-978. | JFM | MR | Zbl

[9] R.T. Rockafellar, Minimax theorems and conjugate saddle-functions, Math. Scand. 14 (1964), 151-173. | MR | Zbl

[10] R.T. Rockafellar, A general correspondence between dual minimax problems and convex programs, Pacific J. Math. 25 (1968), 597-611. | MR | Zbl

[11] C.L. Siegel, Symplectic geometry, Amer. J. Math. 65 (1943), 1-86. | MR | Zbl

[12] O. Thorin, Convexity theorems generalizing those of M. Riesz and Hadamard with some applications, Medd. Lunds Univ. Mat. Sem. 9 (1948), 1-58. | MR | Zbl