关于非交换环面的谱不变性
On spectral invariance of non-commutative tori
摘要：
大约在1980年，康纳斯将几何学的概念扩展到非交换的情形。从那时起{ \it非交换几何}已成为一个非常活跃的数学研究领域。作为非交换流形的第一个非平凡例子，康纳斯讨论了旋转代数的子代数，即所谓的{ \it非交换环面}。在过去的二十年里，研究人员揭示了非交换环面在各种数学和物理领域的相关性。在最近的一篇论文中，我们指出，非交换环面出现在Gabor分析非常自然。在本文中，我们表明，詹森的结果良好的窗口类的Gabor分析已经证明了在一个完全不同的背景下，并在一个非常伪装的形式由Connes在1980年。我们的治疗依赖于非交换类似物的维纳引理的某些子代数的旋转代数的Gröchenig和Leinert。
英文摘要：
Around 1980 Connes extended the notions of geometry to the non-commutative setting. Since then {\it non-commutative geometry} has turned into a very active area of mathematical research. As a first non-trivial example of a non-commutative manifold Connes discussed subalgebras of rotation algebras, the so-called {\it non-commutative tori}. In the last two decades researchers have unrevealed the relevance of non-commutative tori in a variety of mathematical and physical fields. In a recent paper we have pointed out that non-commutative tori appear very naturally in Gabor analysis. In the present paper we show that Janssen's result on good window classes in Gabor analysis has already been proved in a completely different context and in a very disguised form by Connes in 1980. Our treatment relies on non-commutative analogs of Wiener's lemma for certain subalgebras of rotation algebras by Gröchenig and Leinert.
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