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Abstract and Applied Analysis
Volume 2011, Article ID 790728, 13 pages
Research Article

On the Completeness of the System { 𝑧 πœ† 𝑛 l o g 𝑗 𝑧 } in 𝐿 2 π‘Ž

Department of Mathematics, Kunming University of Science and Technology, Kunming 650093, China

Received 8 April 2011; Accepted 13 July 2011

Academic Editor: Allan C. Peterson

Copyright Β© 2011 Xiangdong Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 𝐿 2 π‘Ž ( Ξ© ) denote a Hilbert space consisting of analytic functions on an unbounded domain Ξ© located outside an angle domain with vertex at the origin. We obtain a completeness theorem for the system 𝑀 Ξ› = { 𝑧 πœ† 𝑛 l o g 𝑗 𝑧 , 𝑗 = 0 , 1 , … , π‘š 𝑛 βˆ’ 1 } ∞ 𝑛 = 1 , in 𝐿 2 π‘Ž ( Ξ© ) .