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1.
A. M. Sedletskii 《Mathematical Notes》1995,58(4):1084-1093
We construct real separable sequences {
n
} such that the corresponding systems of exponentials exp(i
n
t) are complete and minimal, but not uniformly minimal, in the spacesL
p
(–, ), 1p<, orC[–, ].Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 582–595, October, 1995.The work was supported by the Russian Foundation for Basic Research under grant No. 93-011-205 相似文献
2.
A. M. Sedletskii 《Mathematical Notes》1977,22(6):941-947
Conditions on the closeness of real sequences {n} and {n} are studied which imply the equality of the excesses of the systems {exp(inx)} and {exp(inx)} in the space L2(–a, a). A theorem is formulated in terms of the difference of the sequences {n} and {n} enumerating the functions. In the corollaries of the theorem, conditions are given in terms of the behavior of the difference n–n0. An example is constructed showing that the condition n–n0 alone is not sufficient for equality of the excesses.Translated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 803–814, December, 1977. 相似文献
3.
A. M. Sedletskii 《Mathematical Notes》2000,68(5-6):602-613
As is well known, the asymptotics of zeros of functions of Mittag--Leffler type $$E_\rho \left( {z;\mu } \right) = \sum\limits_{n = 0}^\infty {\frac{{z^n }}{{\Gamma \left( {\mu + {n \mathord{\left/ {\vphantom {n \rho }} \right. \kern-\nulldelimiterspace} \rho }} \right)}}} ,{\text{ }}\rho >0,{\text{ }}\mu \in \mathbb{C},$$ describes the behavior of zeros outside a disk of sufficiently large radius. In the paper we solve the problem of finding the number of zeros inside such a disk; this allows us to indicate the numeration of all zeros $E_\rho \left( {z;\mu } \right)$ that agrees with the asymptotics. We study the problem of the distribution of zeros of two functions that can be expressed in terms of $E_1 \left( {z;\mu } \right)$ , namely of the incomplete gamma-function and of the error function. 相似文献
4.
5.
A. M. Sedletskii 《Siberian Mathematical Journal》1990,31(5):802-809
Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 120–127, September–October, 1990. 相似文献
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9.
A. M. Sedletskii 《Moscow University Mathematics Bulletin》2007,62(1):22-28
Let z n denote the sequence of zeros of the Mittag-Leffler function E ρ (z; μ), ρ > 0, μ ∈ ?, which is an entire function of order ρ. With the exception of the case ρ = 1/2, Re μ = 3 an asymptotic behavior of the sequence z n ρ was known earlier up to infinitesimals o(1) having a sharply defined rate of decrease. In this paper the behavior of the sequence z n 1/2 is studied just in this exceptional case. Furthermore, for ρ = 1/2, μ > 3 we give the form of a curvilinear half-plane which is free of the points z n . 相似文献
10.
Doklady Mathematics - 相似文献