Geodesic
Bernstein’s analyticity theorem for quantum differences
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 67-73.

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We consider real valued functions $f$ defined on a subinterval $I$ of the positive real axis and prove that if all of $f$’s quantum differences are nonnegative then $f$ has a power series representation on $I$. Further, if the quantum differences have fixed sign on $I$ then $f$ is analytic on $I$.
Classification : 26A24, 26A48, 26E05
Keywords: difference; quantum difference; quantum derivative; power series 
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     author = {Sj\"odin, Tord},
     title = {Bernstein{\textquoteright}s analyticity theorem for quantum differences},
     journal = {Czechoslovak Mathematical Journal},
     pages = {67--73},
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     number = {1},
     year = {2007},
     mrnumber = {2309949},
     zbl = {1174.26312},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007__57_1_a5/}
}
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Sjödin, Tord. Bernstein’s analyticity theorem for quantum differences. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 67-73. http://geodesic.mathdoc.fr/item/CMJ_2007__57_1_a5/