Vrkoč, Ivo Holomorphic extension of a function whose odd derivatives are summable. (English) Zbl 0581.30024 Czech. Math. J. 35(110), 59-65 (1985). If I is a real interval, \(f\in C^{\infty}(I)\), and lim inf\(| f^{(2n+1)}(t)| \geq c>0\) for \(t\in I\) then f is the restriction of an entire function. [This could be derived more briefly from the known result that if the radius of convergence of the Taylor series of f at each point is uniformly bounded away from 0 then f is the restriction to I of an analytic function. For a short proof of this result see H. Salzmann and K. Zeller, Math. Z. 62, 354-367 (1955; Zbl 0064.299)]. Reviewer: R.P.Boas Cited in 1 Document MSC: 30D20 Entire functions of one complex variable (general theory) 26E10 \(C^\infty\)-functions, quasi-analytic functions 26E05 Real-analytic functions Citations:Zbl 0064.299 PDFBibTeX XMLCite \textit{I. Vrkoč}, Czech. Math. J. 35(110), 59--65 (1985; Zbl 0581.30024) Full Text: DOI EuDML References: [1] J. Fischer P. Kolář: On the Validity and Practical Applicability of Derivative Analyticity Relations. J. Math. Phys. 25 (1984), 2538-2544. · doi:10.1063/1.526438 [2] I. P. Natanson: Teorija funkcij veščestvennoj peremennoj. Gosud. Izd. Tech.-Teor. Lit. Moskva 1950. · Zbl 0091.05404 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.