论文标题
特殊词典的希尔伯特空间中具有规定系数的贪婪扩展
Greedy expansions with prescribed coefficients in Hilbert spaces for special classes of dictionaries
论文作者
论文摘要
V. N. Temlyakov在Banach空间的框架中引入了带有规定系数的贪婪扩张。这个想法是选择一系列固定（真）系数$ \ {c_n \} _ {n = 1}^\ infty $和Banach Space的固定元素（字典）;然后，在系数和字典的适当条件下，可以将Banach空间的所有元素串联扩展，这些元素仅包含固定系数和字典的元素。在希尔伯特（Hilbert）空间中，贪婪算法与规定系数的收敛性是特征的，从某种意义上说，系数上存在必要和足够的条件，以便该算法对所有字典都收敛。本文涉及一个问题，是否可以削弱特定的空间或字典类别的条件；我们证明有限维空间是这种情况，对于与无限尺寸空间中正常序列相关的某些类似词典。
Greedy expansions with prescribed coefficients have been introduced by V. N. Temlyakov in the frame of Banach spaces. The idea is to choose a sequence of fixed (real) coefficients $\{c_n\}_{n=1}^\infty$ and a fixed set of elements (dictionary) of the Banach space; then, under suitable conditions on the coefficients and the dictionary, it is possible to expand all the elements of the Banach space in series that contain only the fixed coefficients and the elements of the dictionary. In Hilbert spaces the convergence of greedy algorithm with prescribed coefficients is characterized, in the sense that there are necessary and sufficient conditions on the coefficients in order that the algorithm is convergent for all the dictionaries. This paper is concerned with the question if such conditions can be weakened for particular classes of spaces or dictionaries; we prove that this is the case for finite dimensional spaces, and for some classes of dictionaries related to orthonormal sequences in infinite dimensional spaces.
