Related papers: Noncommutative extensions of the Fourier transform…
We formulate non-relativistic classical and quantum mechanics in the non-commutative two dimensional plane. The approach we use is based on the Galilei group, where the non-commutativity is seen as a central extension upon identification of…
Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…
We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for…
We develop a functional calculus for $d$-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra.
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained…
We present definitions for real and quaternionic second-order free cumulants, functions whose collective vanshing when applied to elements from different subalgebras is equivalent to the second-order real (resp.\ quaternionic) freeness of…
Operator representation of Cole-Hopf transform is obtained based on the logarithmic representation of infinitesimal generators. For this purpose the relativistic formulation of abstract evolution equation is introduced. Even independent of…
We consider the group $(\mathcal{G},*)$ of unitized multiplicative functions in the incidence algebra of non-crossing partitions, where ``$*$'' denotes the convolution operation. We introduce a larger group $(\widetilde{\mathcal{G}},*)$ of…
It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…
We show that the $\star$-product for $U(su_2)$, group Fourier transform and effective action arising in [1] in an effective theory for the integer spin Ponzano-Regge quantum gravity model are compatible with the noncommutative bicovariant…
We investigate and review how Fourier transform is involved in the analysis of a twisted group algebra $L^1(G, \sigma)$ for $G=\widehat{\Gamma}\times \Gamma$ and $\sigma:G\times G \to \mathbb{T}$ 2- cocycle where $\Gamma$ is a locally…
In this work we extend the recently introduced group-theoretical approach to moment-cumulant relations in non-commutative probability theory to the notion of conditionally free cumulants. This approach is based on a particular combinatorial…
Let $M$ be a finite dimensional modular representation of a finite group $G$. We consider the generating function for the non-projective part of the tensor powers of $M$, and we write $\gamma_G(M)$ for the reciprocal of the radius of…
A simple connection between the universal $R$ matrix of $U_q(sl(2))$ (for spins $\demi$ and $J$) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an…
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…
We introduce a multiparametric quantum superspace with $m$ even generators and $n$ odd generators whose commutation relations are in the sense of Manin such that the corresponding algebra has a Hopf superalgebra. By using its Hopf…
The representations of Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under noncommutative phase space transformations is constructed.…
By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group $\mathbb{G}$ a completely contractive Banach algebra $A_\Delta(\mathbb{G})$, which can be viewed as a deformed Fourier…
We study, to certain Banach spaces $X$, families of weighted composition operators. Notably, we show that if this family form a strongly continuous semigroup, then its infinitesimal generator ($\Gamma, D(\Gamma)$) is given by $\Gamma f =…
Let $T\colon H^1({\mathbb R})\to H^1({\mathbb R})$ be a bounded Fourier multiplier on the analytic Hardy space $H^1({\mathbb R})\subset L^1({\mathbb R})$ and let $m\in L^\infty({\mathbb R}_+)$ be its symbol, that is,…