Nonasymptotic properties of roots of a Mittag-Leffler type function

Mathematical Notes

Volumn 75, Issue 3-4, 2004, Pages 372-386

  Sedletskii, A M ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Cauchy type integral; Distribution of roots; Entire function; Hurwitz theorem; Mittag Leffler function; Multiple root; Simple root

Indexed keywords

EID: 3543116108     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:matn.0000023316.90489.fe     Document Type: Article

References (17)

1. M. M. Dzhrbashyan, Integral Transforms and Representations of Functions in the Complex Domain [in Russian], Nauka, Moscow, 1966.
2. α(x)," C. R. Acad. Sci. Paris. Ser. 2, 137 (1903), 554-558.
3. A. M. Sedletskii, "Asymptotic formulas for zeros of functions of Mittag-Leffer type," Anal. Math., 20 (1994), 117-132.
4. α(x)," Acta Math., 29 (1905), 217-234.
5. α(z)," Tôhoku Math. J., 19 (1921), 241-248.
6. M. M. Dzhrbashyan, "Interpolational and spectral decompositions associated with differential operators of fractional order," Izv. Akad. Armyan. SSR Ser. Mat. [Soviet J. Contemporary Math. Anal.], 19 (1984), 81-181.
7. M. M. Djrbashian, Harmonic Analysis and Boundary-Value Problems in the Complex Domain, Birkhäuser Verlag, Basel-Boston-Berlin, 1993.
8. ρ(z; μ)," Anal. Math., 23 (1997), 283-296.
9. A. Yu. Popov, "On the Ostrovskii-Peresyolkova conjecture about zeros of the Mittag-Leffer functions," Proc. Steklov Inst. Math. (2001), Suppl. 1, 167-182.
10. A. Yu. Popov, "Spectral values of a boundary-value problem and zeros of Mittag-Leffer functions," Differentsial'nye Uravneniya [Differential Equations], 38 (2002), no. 5, 611-621.
11. M. M. Dzhrbashyan and A. B. Nersesyan, "Construction of some special biorthogonal systems," Izv. Akad. Armyan. SSR Ser. Mat. [Soviet J. Contemporary Math. Anal.], 12 (1959), 17-42.
12. A. M. Sedletskii, "Zeros of a Mittag-Leffer type function," Mat. Zametki [Math. Notes], 68 (2000), no. 5, 710-724.
13. A. M. Nakhushev, Elements of Fractional Calculus and Their Application [in Russian], Izd. KBNTs RAN, Nalchik, 2000.
14. A. M. Sedletskii, "Approximation properties of systems of exponentials on a line and a half-line," Mat. Sb. [Russian Acad. Sci. Sb. Math.], 189 (1998), 125-140.
15. I. Z. Tikhonov and Yu. S. Éidel'man, "Inverse scattering transform for differential equations in Banach space and the distribution of zeros of an entire Mittag-Leffer type function," Differentsial'nye Uravneniya [Differential Equations], 38 (2002), no. 5, 637-644.
16. A. I. Markushevich, The Theory of Analytic Functions [in Russian], vol. 1, Nauka, Moscow, 1967.
17. G. Polya and G. Szego, Problems and Theorems in Analysis, vol. 1, Springer-Verlag, Berlin, 1972.