论文标题
组的热能
Heat properties for groups
论文作者
论文摘要
我们在（扭曲的）降低组C* - 代数，傅立叶级数的收敛和与负定确定功能相关的半群中求解圆圈上的热方程的方法。我们引入了一些无数群体的热特性，并调查何时满足它们。 Kazhdan的财产（T）是对最薄弱的财产的阻碍，我们的发现使这可能是唯一的可能性。另一方面，许多拥有Haagerup属性的团体都满足最强的版本。我们表明，这种热量特性意味着相关的热问题具有独特的解决方案，而不管最初的基准的选择如何。
We revisit Fourier's approach to solve the heat equation on the circle in the context of (twisted) reduced group C*-algebras, convergence of Fourier series and semigroups associated to negative definite functions. We introduce some heat properties for countably infinite groups and investigate when they are satisfied. Kazhdan's property (T) is an obstruction to the weakest property, and our findings leave open the possibility that this might be the only one. On the other hand, many groups with the Haagerup property satisfy the strongest version. We show that this heat property implies that the associated heat problem has a unique solution regardless of the choice of the initial datum.
