关于Lax-Phillips半群
On Lax-Phillips semigroups
摘要：
Lax-Phillips演化由两个空间散射系统描述。正则识别算子的特点是拉克斯-菲利普斯演化，其传出和传入的投影交换。在这种情况下，可以引入（广义）Lax-Phillips半群，并考虑它的谱理论。在Lax和Phillips最初考虑的特殊情况下（其中传出和传入子空间相互正交），这个半群与Lax和Phillips引入的半群一致。在更一般的情况下，半群的存在性不与散射矩阵在上半平面中的（整体）全纯连续性相耦合。强调了Lax-Phillips半群与所谓的参考演化特征半群的基本联系。
英文摘要：
Lax-Phillips evolutions are described by two-space scattering systems. The canonical identification operator is characterized for Lax-Phillips evolutions, whose outgoing and incoming projections commute. In this case a (generalized) Lax-Phillips semigroup can be introduced and its spectral theory is considered. In the special case, originally considered by Lax and Phillips (where the outgoing and incoming subspaces are mutually orthogonal), this semigroup coincides with that introduced by Lax and Phillips. In the more general case the existence of the semigroup is not coupled with the (global) holomorphic continuability of the scattering matrix into the upper half plane. The basic connection of the Lax-Phillips semigroup to the so-called characteristic semigroup of the reference evolution is emphasized.
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