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gap theorems; lacunary series; power sum method
By combining Turán’s proof of Fabry’s gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.
[1] Landau L.: Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie. Berlin 1929.
[2] Turán P.: On the gap-theorem of Fabry. Acta Math. Sci. Acad. Hung. 1 (1947), 21–29. MR 0022905 | Zbl 0029.39302
[3] Turán P.: On a new method of analysis and its applications. Wiley-Interscience Publication, New York etc. (1984). MR 0749389 | Zbl 0544.10045
[4] Szüsz P.: On Hadamard’s gap theorem. Studies in pure mathematics to the memory of Paul Turán, Budapest 1983, 733–736. MR 0820266 | Zbl 0523.30001
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