论文标题
迭代框架和矢量值模型空间
Frames of iterations and vector-valued model spaces
论文作者
论文摘要
令T为Hilbert Space H上的一个有界的操作员，而F = {f_j：j in J}是H中最可数的矢量集。在本注中，我们表征了{t，f}对{t^n f：f in}的{t^n f：f：in i}中的f，i}的f in i = n_0 and i = z.0和i = z i = z i = z. = z.0 = n_0 and i = z.的表征，在单位磁盘上定义的分析函数耐力空间的模型空间上的移位作用在$ l^2（j）中的值。这将概括为单个功能的迭代术。在双边迭代的情况下，表征是通过作用于l^2（t，l^2（j））的双侧偏移。 此外，我们表征了当j是有限的，分别在单侧和双侧情况下，j是有限的，而j是有限的。最后，我们研究了在这种情况下发现产生框架的轨道数量最少的问题。
Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0 and I = Z. The characterization for unilateral iterations gives a similarity with the compression of the shift acting on model spaces of the Hardy space of analytic functions defined on the unit disk with values in $l^2(J). This generalizes recent work for iterations of a single function. In the case of bilateral iterations, the characterization is by the bilateral shift acting on doubly invariant subspaces of L^2(T,l^2(J)). Furthermore, we characterize the frames of iterations for vector-valued model operators when J is finite in terms of Toeplitz and multiplication operators in the unilateral and bilateral case, respectively. Finally, we study the problem of finding the minimal number of orbits that produce a frame in this context.
