Möbius transformations and monogenic functional calculus
Möbius transformations and monogenic functional calculus
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莫比乌斯变换和单基因泛函计算
DOI：
10.1090/s1079-6762-96-00004-2
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
V. Kisil
中科院分区：
文献类型：
--
作者：
V. Kisil
提出了一种计算泛函演算的新方法。泛函演算Φ：f(X)→f(T)不是泛函代数到算子代数的代数同态，而是作用于这两个代数(作为线性空间)的群的两个表示之间的交织算子。对于任意一组非交换自伴算子，我们在新发展的单基因泛函演算上证明了这一方案。给出了相应的谱和谱映射定理。
A new way of doing functional calculi is presented. A functional calculus Φ : f(x) → f(T ) is not an algebra homomorphism of a functional algebra into an operator algebra, but an intertwining operator between two representations of a group acting on the two algebras (as linear spaces). This scheme is shown on the newly developed monogenic functional calculus for an arbitrary set of non-commuting self-adjoint operators. The corresponding spectrum and spectral mapping theorem are included.