Bounded and continuous random Fourier series on non- commutative groups

Non-commutative automorphisms of bounded non-commutative domains

We establish rigidity (or uniqueness) theorems for nc automorphisms which are natural extensions of clasical results of H. Cartan and are improvements of recent results. We apply our results to ncdomains consisting of unit balls of rectangular matrices.

Lacunary Fourier Series on Noncommutative Groups

Non-commutative tori and Fourier–Mukai duality

The classical Fourier–Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to an equivalence between two dual objects. Both of these are generalized deformations of the complex tori. In one case, a complex torus is deformed formally in a non-commutative direction specified by ...

Continuous-time random walks on bounded domains.

A useful perspective to take when studying anomalous diffusion processes is that of a continuous-time random walk and its associated generalized master equation. We derive the generalized master equations for continuous-time random walks that are restricted to a bounded domain and compare numerical solutions with kernel-density estimates of the probability-density function computed from simulat...

On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups

Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|...