On Zeros of Entire Functions of Special Form
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 24-31.

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Sufficient conditions for an entire function of special form to have no zeros in the open lower half-plane are obtained.
Keywords: entire function, distribution of zeros of functions, real function, real function of bounded variation, positive definite function, absolutely continuous function.
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V. P. Zastavnyi. On Zeros of Entire Functions of Special Form. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 24-31. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a2/

[1] A. F. Leontev, Ryady eksponent, Nauka, M., 1976 | MR | Zbl

[2] E. Lukach, Kharakteristicheskie funktsii, Nauka, M., 1979 | MR | Zbl

[3] A. M. Sedletskii, “O tselykh funktsiyakh klassa S. N. Bernshteina, ne yavlyayuschikhsya preobrazovaniyami Fure–Stiltesa”, Matem. zametki, 61:3 (1997), 367–380 | MR | Zbl

[4] I. V. Tikhonov, “Teoremy edinstvennosti v lineinykh nelokalnykh zadachakh dlya abstraktnykh differentsialnykh uravnenii”, Izv. RAN. Ser. matem., 67:2 (2003), 133–166 | MR | Zbl

[5] R. M. Trigub, E. S. Belinsky, Fourier Analysis and Approximation of Functions, Kluwer Acad. Publ., Boston–Dordrecht–London, 2004 | MR | Zbl

[6] G. H. Hardy, “On the zeroes of certain classes of integral Taylor series. Part II. On the integral function $\sum_{n=0}^\infty x^n/((n+a)^sn!)$ and other similar functions”, Proc. London Math. Soc. Ser. 2, 2:1 (1905), 401–431 | DOI | Zbl

[7] G. Polya, “Über die nullstellen gewisser ganzer funktionen”, Math. Z., 2:3–4 (1918), 352–383 | DOI | MR | Zbl

[8] E. C. Titchmarsh, “The zeros of certain integral functions”, Proc. London Math. Soc. Ser. 2, 25:1 (1926), 283–302 | DOI | MR | Zbl

[9] M. Cartwright, “The zeros of certain integral functions”, Quart. J. Math., 1:1 (1930), 38–59 | DOI | MR | Zbl

[10] M. Cartwright, “The zeros of certain integral functions. (II)”, Quart. J. Math., 2:1 (1931), 113–129 | DOI | MR | Zbl

[11] A. M. Sedletskii, “On zeros of Laplace transforms of finite measure”, Integral Transform. Spec. Funct., 1:1 (1993), 51–59 | DOI | MR | Zbl

[12] A. M. Sedletskii, “O nulyakh preobrazovanii Laplasa”, Matem. zametki, 76:6 (2004), 883–892 | MR | Zbl

[13] V. P. Zastavnyi, “Teorema o nulyakh tselykh funktsii i ee primenenie”, Matem. zametki, 75:2 (2004), 192–207 | MR | Zbl

[14] V. P. Zastavnyi, “A theorem on zeros of an entire function and its applications”, Methods Funct. Anal. Topology, 10:2 (2004), 91–104 | MR | Zbl

[15] N. I. Akhiezer, Lektsii ob integralnykh preobrazovaniyakh, Vischa Shkola, Kharkov, 1984 | MR | Zbl

[16] I. Stein, G. Veis, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | MR | Zbl

[17] V. P. Zastavnyi, “On positive definiteness of some functions”, J. Multivariate Anal., 73:1 (2000), 55–81 | DOI | MR | Zbl