A remark on basis property of systems of Bessel and Mittag-Leffler type functions
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- 作者：B. V. Vynnyts’kyi ; R. V. Khats’
- 关键词：Entire function of exponential type ; Bessel function ; Mittag ; Leffler ; type function ; basis ; complete system ; minimal system ; biorthogonal system
- 刊名：Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
- 出版年：2015
- 出版时间：November 2015
- 年：2015
- 卷：50
- 期：6
- 页码：300-305
- 全文大小：610 KB
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R. V. Khats’ (1)
1. Ivan Franko State Pedagogical University, Drohobych, Ukraine - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Russian Library of Science - 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
- ISSN：1934-9416
文摘
We find sufficient conditions for the basisness of the system (\(\sqrt {x\rho k} {J_v}\left( {x\rho k} \right):k \in N\)) in the space L 2(0; 1) and establish a relationship between the approximation properties of this system and the properties of the system (τ ν+1/2E1/2(−τ 2 ρ k 2 ; μ): k ∈ N), where J ν is the Bessel function of the first kind of index ν and E ρ (z; μ) is the Mittag-Leffler-type function. Keywords Entire function of exponential type Bessel function;Mittag-Leffler-type function basis complete system minimal system biorthogonal system