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应用数学学报  1996, Vol. 19 Issue (4): 481-488    DOI:
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多元样本定理及混淆误差的估计
王建军, 房艮孙
北京师范大学数学系, 北京100875
MULTIDIMENSIONAL SAMPLING THEOREM AND ESTIMATE OF ALIASING ERROR
WANG JIANJUN, FANG GENSUN
Department of Mathematics, Beijing Normal University, Beijing, 100875
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摘要 本文证明了多元指数型整函数的一个Marcinkiewicz型不等式,并由此证得了多元Whittaker-Kotelnikov-Shannon型的样本定理,从而得到了多元Sobolev类上的混淆误差界的阶的精确估计.
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王建军
房艮孙
关键词多元样本定理   指数型整函数   混淆误差     
Abstract: In this paper,we prove an Marcinkiewicz type inequality of entire functions of exponential type,and from this result,we obstain the Whittaker-Kotelnikov-Shannon type sampling theorem of multiply variables and determine the abasing error on the Sobolev classes.
Key wordsSampling theorem of multiply variables   entire function of exponential   type abasing error   
收稿日期: 1995-01-24;
基金资助:国家教委博士点基金
引用本文:   
王建军,房艮孙. 多元样本定理及混淆误差的估计[J]. 应用数学学报, 1996, 19(4): 481-488.
WANG JIANJUN,FANG GENSUN. MULTIDIMENSIONAL SAMPLING THEOREM AND ESTIMATE OF ALIASING ERROR[J]. Acta Mathematicae Applicatae Sinica, 1996, 19(4): 481-488.
 
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