Geodesic
Almost periodic functions in finite-dimensional space with the spectrum in a cone
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 3, pp. 465-477 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that an almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. We also prove that an almost periodic function in finite-dimensional space has the bounded spectrum if and only if it extends to an entire function of exponential type. 
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     author = {S. Favorov and O. Udodova},
     title = {Almost periodic functions in finite-dimensional space with the spectrum in a cone},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {465--477},
     year = {2002},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2002_9_3_a14/}
}
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S. Favorov; O. Udodova. Almost periodic functions in finite-dimensional space with the spectrum in a cone. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 3, pp. 465-477. http://geodesic.mathdoc.fr/item/JMAG_2002_9_3_a14/