| Completeness of the system {z^λn} in L^2[B,α0] |
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| 作者姓名： | Ju Hong NING ;Guan Tie DENG |
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| 作者单位： | [1]Department of Mathematics, Jiangxi Normal University, Nanchang 330022, P. R. China; [2]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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| 基金项目： | The first author is supported partially by Natural Science Foundation of Jiangxi Province （Grant No. 2007GQS0159） and Research Plan Programm of Jiangxi Provincial Department of Education （Grant No.G J J08161）; The second author is supported partially by Grant No. 10371011 of the NSFC. Acknowledgments The authors are grateful to the anonymous referees for their helpful suggestions and comments which have improve the quality of the paper. |
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| 摘 要： | Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}（n = 1,2,...） be a sequence of complex numbers satisfying sup ｜ arg（λn）｜ 〈 α 〈 π/2 and denote by M（∧） = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ（λ∈∧）. Let α0（z） be a weight function defined on B. We obtain a completeness theorem for the system M（∧） in the Hilbert space L^2 B, α0].
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| 关 键 词： | Hilbert空间 极大域 完备性 泛函分析 |
Completeness of the system
\{ z^{\lambda _n } \}
in L
2[B,α
0] |
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| Ju Hong NING,;Guan Tie DENG.Completeness of the system
\{ z^{\lambda _n } \}
in L
2[B,α
0][J].Acta Mathematica Sinica,2008,24(12):2101-2110. |
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| Authors: | Ju Hong Ning Guan Tie Deng |
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| Institution: | (1) Department of Mathematics, Jiangxi Normal University, Nanchang, 330022, P. R. China;(2) School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China |
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| Abstract: | Let B be an unbounded domain located outside an angle domain with vertex at the origin, Λ = {λ
nn
}(n = 1, 2, ...) be a sequence of complex numbers satisfying sup | arg(λ
n
)| < α < π/2 and denote by M(Λ) = {z
λ, λ ∈ Λ} the corresponding system of functions z
λ(λ ∈ Λ). Let α
0(z) be a weight function defined on B. We obtain a completeness theorem for the system M(Λ) in the Hilbert space L
2B,α
0].
The first author is supported partially by Natural Science Foundation of Jiangxi Province (Grant No. 2007GQS0159) and Research
Plan Programm of Jiangxi Provincial Department of Education (Grant No.GJJ08161); The second author is supported partially
by Grant No. 10371011 of the NSFC |
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| Keywords: | completeness unbounded domain Hilbert space |
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