DISCRETE CONVOLUTION OPERATORS ON THE QUARTER PLANE AND THEIR INDICES
DISCRETE CONVOLUTION OPERATORS ON THE QUARTER PLANE AND THEIR INDICES
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四分之一平面上的离散卷积算子及其索引
DOI：
10.1070/im1977v011n05abeh001759
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发表时间：
1977
期刊：
影响因子：
--
通讯作者：
R. V. Dudučava
中科院分区：
文献类型：
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作者：
R. V. Dudučava
设，其中为单位圆，设为向量值函数的Hilbert空间，其分量为上的复值平方可积函数。本文考虑函数在环面上的解析延拓的子空间，设为上的投影。对于有界可测的阶矩阵值函数，在有极限和(一致在)上定义有界算子。本文给出了一种计算Noether算子在由其生成的代数中的指数的同伦方法。在连续的情况下，给出了一个简单的计算索引的公式。参考书目：24种。
Let , where is the unit circle, and let be the Hilbert space of vector-valued functions whose components are complex-valued square integrable functions on . The author considers the subspace of functions in having analytic continuations into the torus ; let be the projection of onto . For a bounded measurable matrix-valued function of order on having limits and ( uniform in , the bounded operator is defined in . In this paper a homotopy method is described for computing the index of Noetherian operators in the -algebra generated by the operators . In the case where is continuous a simple formula for computing the index of is indicated.Bibliography: 24 titles.