AI 中文总结
研究再生核的贝林准则，通过多种方式刻画贝林 - 拉克斯 - 哈尔莫斯（BLH）再生核对类别，统一扩展相关结果，举例说明理论并与完全皮卡对研究对比，指出完全皮卡核类别与BLH核类别反向包含关系不成立。
AI 中文摘要
一个由贝林 - 拉克斯 - 哈尔莫斯提出的经典定理，将单边移位的不变子空间刻画为作用在哈代空间上的等距乘法算子的值域。引入了贝林 - 拉克斯 - 哈尔莫斯（BLH）再生核对的类别，其中包含那些承认该定理类似物的对。在不同假设下，BLH类别通过多种等价方式进行刻画：从扩张理论角度、通过完全李希插值性质以及基于平方和启发的阿格勒式分解。这些刻画统一并扩展了文献中的各种相关结果。给出例子来说明该理论、假设，并与完全皮卡对研究的最新进展进行比较和对比。特别地，虽然预计在某些温和假设下，完全皮卡核的类别包含在BLH核的类别中，但结果表明反向包含在很强的意义上不成立。
英文摘要
A classical theorem due to Beurling-Lax-Halmos characterizes the invariant subspaces of the unilateral shift as ranges of isometric multiplication operators acting on the Hardy space. The class of Beurling-Lax-Halmos (BLH) pairs of reproducing kernels is introduced, consisting of those pairs that admit an analogue of this theorem. The BLH class is, under varying hypotheses, characterized in several equivalent ways: dilation-theoretically, via a complete Leech interpolation property, and through a sums-of-squares-inspired Agler-style decomposition. These characterizations unify and extend a variety of related results in the literature. Examples are given to illustrate the theory, the hypotheses and compare and contrast with the recent developments in the study of complete Pick pairs. In particular, while it is anticipated, perhaps under some mild assumptions, that the class of complete Pick pairs of kernels is contained in the class of BLH pairs of kernels, it is shown that the reverse inclusion fails in a strong sense.
CommentsVarious tweaks and fixes throughout
