Twisted Fourier analysis and pseudo-probability distributions

Fourier series and twisted C*-crossed products

This paper is an invitation to Fourier analysis in the context of reduced twisted C*-crossed products associated with discrete unital twisted C*-dynamical systems. We discuss norm-convergence of Fourier series, multipliers and summation processes. Our study relies in an essential way on the (covariant and equivariant) representation theory of C*-dynamical systems on Hilbert C*-modules. It also yields some information on the ideal structure of reduced twisted C*-crossed products.

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, Følner nets give the key to Fejér summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable gr…

Twisted Pseudo-differential Operators on Type I Locally Compact Groups

Let $\G$ be a locally compact group satisfying some technical requirements and $\wG$ its unitary dual. Using the theory of twisted crossed product $C^*$-algebras, we develop a twisted global quantization for symbols defined on $\G\times\wG$ and taking operator values. The emphasis is on the representation-theoretic aspect. For nilpotent Lie groups, the connection is made with a scalar quantization of the cotangent bundle $T^*(\G)$ and with a Quantum Mechanical theory of observables in the presence of variable magnetic fields.

在扭曲的Hilbert尺度上应用Fredholm理论：一种框架理论方法用于半整数傅里叶模式

Fredholm Theory on Twisted Hilbert Scales: A Frame-Theoretic Approach to Half-Integer Fourier Modes

本文通过框架理论方法，在扭曲的Hilbert尺度上构建了一个具有半整数傅里叶模式的Fredholm算子，并证明其在相邻尺度层级间具有零索引的Fredholm映射。

Bi-conformal vector fields and the local geometric characterization of conformally separable (double-twisted) pseudo-Riemannian manifolds

This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.} \textbf{21}, 2153-2177 and some of their basic properties were addressed there. In our calculations a new affine connection ({\em bi-conformal connection}) arises quite naturally and this connection enables us to find a local characterization of {\em conformally separable} pseudo-Riemannian manifolds (also called double twisted pro…

从几乎交换几何中的扭曲谱三元体中涌现时间

Emergence of Time from a Twisted Spectral Triple in Almost-Commutative Geometry

本文探讨了在几乎交换框架内，扭曲谱三元体如何产生伪黎曼结构，并提出了一种统一的代数机制解决洛伦兹签名问题，通过连接扭曲与伪黎曼谱三元体的映射概念，提供了替代温克旋转的方法。