| 酉群上的三角多项式不变算子 |
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| 引用本文： | 郑兵.酉群上的三角多项式不变算子[J].安徽大学学报(自然科学版),1988(4). |
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| 作者姓名： | 郑兵 |
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| 作者单位： | 安徽大学数学系 |
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| 摘 要： | 本文主要证明n阶酉群U_n上Fourier级数部分和所决定的算子SN(f)的范数就等于U_n上的Lebesgue常数,且证明U_n上的Faber-Marcinkiewiez公式的Berman推广也是成立的。作为推论同时也说明了算子S_N(f)在三角多项式不变算子类mN中具有最小的范数以及对于任意的算子L_N∈mN(N=1,2,…),序列L_N(f)不能在全空间C(U_n)中收敛。
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| 关 键 词： | Lebesgue常数 三角多项式不变算子 |
Trigonometric Polynomial Invariant Operators On Unitary Groups |
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| Zheng Bing.Trigonometric Polynomial Invariant Operators On Unitary Groups[J].Journal of Anhui University(Natural Sciences),1988(4). |
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| Authors: | Zheng Bing |
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| Abstract: | In this paper, We first proved that the norms of Fourier series partial Summation operators S_N(f) on the unitary group of order N are equal to the Lebesgue Constants of Dirichlet kernal D_N(V). For the trigonometric polynomial invarant operator,the paper show the truth of Bermans extension of Faber and Marcinkiewiez formula fn the unitary groups. As their inference, the orperator S_N(f)has the smallest norm in the class of all trigonometric polynomial invarant operat or of order N. |
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| Keywords: | lebesgue constants trigonometric polynomial invarant operator |
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