The Fourier binest algebra
The Fourier binest algebra
复制标题
傅里叶二元代数
DOI：
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发表时间：
1997
影响因子：
0.8
通讯作者：
S. Power
中科院分区：
文献类型：
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作者：
A. Katavolos;S. Power
傅里叶二元嵌套代数被定义为 L2(ℝ) 上的 Volterra 嵌套代数与其共轭傅里叶变换的交集。尽管不存在非零有限秩算子，该代数仍等于希尔伯特-施密特二元解析伪微分算子的弱算子拓扑中的闭包。 （非分配）不变子空间格被确定为 Volterra 和解析巢（傅里叶二元巢）的增强，由与单模函数 exp(−isx2/2) 相关的巢连续统（对于 s>0）。该多重嵌套是傅立叶二元嵌套的自反闭包，并且作为具有弱算子拓扑的拓扑空间，它与单位圆盘同胚。使用此标识，代数的酉自同构群被确定为作用 κt(λ, μ) =(etλ, e−t μ) 的半直积 ℝ2×κℝ。
The Fourier binest algebra is defined as the intersection of the Volterra nest algebra on L2(ℝ) with its conjugate by the Fourier transform. Despite the absence of nonzero finite rank operators this algebra is equal to the closure in the weak operator topology of the Hilbert–Schmidt bianalytic pseudo-differential operators. The (non-distributive) invariant subspace lattice is determined as an augmentation of the Volterra and analytic nests (the Fourier binest) by a continuum of nests associated with the unimodular functions exp(−isx2/2) for s>0. This multinest is the reflexive closure of the Fourier binest and, as a topological space with the weak operator topology, it is shown to be homeomorphic to the unit disc. Using this identification the unitary automorphism group of the algebra is determined as the semi-direct product ℝ2×κℝ for the action κt(λ, μ) =(etλ, e−t μ).