双圆盘上Poletsky-Stessin Hardy空间的Beurling型不变子空间
复变函数
2016-07-27 v2
摘要
单位圆盘上 Hardy空间的不变子空间众所周知，但在多变量中经典Hardy空间的不变子空间结构尚未完全理解。本研究考察Poletsky-Stessin Hardy空间的不变子空间问题，这是经典Hardy空间到中超凸域的自然推广。我们证明并非所有不变子空间都是Beurling型。为刻画该空间的Beurling型不变子空间，我们首先将向量值Hardy空间的Lax-Halmos定理推广到向量值Poletsky-Stessin Hardy空间，然后给出的不变子空间为Beurling型的充要条件。
引用
@article{arxiv.1506.07538,
title = {Beurling-Type Invariant Subspaces of the Poletsky-Stessin Hardy Spaces in the Bidisc},
author = {Beyaz Basak Koca and Sibel Sahin},
journal= {arXiv preprint arXiv:1506.07538},
year = {2016}
}
备注
One of the key lemmata referred to a different author in the previous version had some misleading points so in this new version it is proved differently by the authors for a much more clear representation of the main theorem