Geodesic
A function-algebra variant of a theorem of Bohr–van Kampen
Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 233-243 
E. A. Gorin. A function-algebra variant of a theorem of Bohr–van Kampen. Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 233-243. http://geodesic.mathdoc.fr/item/SM_1970_11_2_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

According to the classical Bohr–von Kampen theorem, if a function on a connected compact group is continuous and has no zeros then it has (to within a character) a continuous logarithm. This theorem can be extended to an arbitrary commutative Banach algebra in whose group of automorphisms a connected compact group is presented. Bibliography: 10 titles.

[1] B. M. Levitan, Pochti-periodicheskie funktsii, Gostekhizdat, Moskva, 1953

[2] A. Veil, Integrirovanie v topologicheskikh gruppakh i ego primeneniya, IL, Moskva, 1950

[3] E. R. van Kampen, “On almost periodic functions of constant absolute value”, J. Lond. Math. Soc., XII:1 (1937), 3–6

[4] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, Moskva, 1962

[5] B. M. Levitan, “K teoreme ob argumente pochti-periodicheskoi funktsii”, Matem. zametki, 1:1 (1967), 35–44 | MR | Zbl

[6] V. Ya. Lin, “Poluinvariantnoe integrirovanie so znacheniyami v gruppe i nekotorye ego primeneniya”, Matem. sb., 82(124) (1970), 233–259 | MR

[7] E. A. Gorin, V. Ya. Lin, Topologicheskii smysl teoremy Bora ob argumente pochti-periodicheskoi funktsii, Tezisy dokl. 5-i Vsesoyuznoi topologich. konferentsii, Novosibirsk, 1967

[8] I. M. Gelfand, D. A. Raikov, G. E. Shilov, Kommutativnye normirovannye koltsa, Fizmatgiz, Moskva, 1960

[9] L. Lyumis, Vvedenie v abstraktnyi garmonicheskii analiz, IL, Moskva, 1956

[10] X. Roiden, “Funktsionalnye algebry”, Matematika, 9:2 (1965), 98–114