Related papers: Hypercontractivity of heat semigroups on free quan…
In this paper, we discuss hypercontractivity for the Markov semigroup $P_t$ which is generated by segment processes associated with a range of functional SDEs of neutral type. As applications, we also reveal that the semigroup $P_t$…
We give locally finite Markov trees in $L^p$-compact$,$ separable Hilbert$,$ supersymmetric process$:$ $[0,\infty)\!\times\!\mathbb{R}^{\lvert\mathcal{A}^{\otimes m}\rvert}/\mathcal{A}^{\otimes m}$ on quantum ${\rm…
We consider quantum electrodynamics in noncommutative spacetime by deriving a $\theta$-exact Seiberg-Witten map with fermions in the fundamental representation of the gauge group as an expansion in the coupling constant. Accordingly, we…
We prove a Schoenberg-type correspondence for non-unital semigroups which generalizes an analogous result for unital semigroup proved by Michael Sch\"urmann. It characterizes the generators of semigroups of linear maps on $M_n(C)$ which are…
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic…
A free semigroup algebra S is the weak-operator-closed (non-self-adjoint) operator algebra generated by n isometries with pairwise orthogonal ranges. A unit vector x is said to be wandering for S if the set of images of x under…
Strongly continuous semigroups of unital completely positive maps (i.e. quantum Markov semigroups or quantum dynamical semigroups) on compact quantum groups are studied. We show that quantum Markov semigroups on the universal or reduced…
We show that the Ornstein-Uhlenbeck semigroup associated with a general Poisson random measure is hypercontractive, whenever it is restricted to non-increasing mappings on configuration spaces. We deduce from this result some versions of…
In this note, we answer a question raised by Johnson and Schechtman \cite{JS}, about the hypercontractive semigroup on $\{-1,1\}^{\NN}$. More generally, we prove the folllowing theorem. Let $1<p<2$. Let $(T(t))_{t>0}$ be a holomorphic…
With appropriate notions of Hermitian vector bundles and connections over weighted graphs which we allow to be locally infinite, we prove Feynman-Kac-type representations for the corresponding semigroups and derive several applications…
A quantum graph $\mathcal{G}$ housed by a matrix algebra $M_n$ can be encoded as an operator system $\mathcal S=\mathcal{S}_{\mathcal{G}}\le M_n$. There are two sensible notions of quantum automorphism group for any such:…
A semigroup (dynamical system) generated by $C^{1+\alpha}$-contracting mappings is considered. We call a such semigroup regular if the maximum $K$ of the conformal dilatations of generators, the maximum $l$ of the norms of the derivatives…
We study the thermodynamic properties of the simplest gauged permutation invariant matrix quantum mechanical system of oscillators, for general matrix size $N$. In the canonical ensemble, the model has a transition at a temperature $T$…
Let $\{\phi_s\}_{s\in S}$ be a commutative semigroup of completely positive, contractive, and weak*-continuous linear maps acting on a von Neumann algebra $N$. Assume there exists a semigroup $\{\alpha_s\}_{s\in S}$ of weak*-continuous…
We prove that $(\lambda_g\mapsto e^{-t|g|^r}\lambda_g)_{t>0}$ defines a completely bounded semigroup of multipliers on the von Neuman algebra of hyperbolic groups for all real number $r$. One ingredient in the proof is the observation that…
For any $1 < p < q < \infty$, we investigate fixed-time hypercontractive bounds from $L^p$ to $L^q$ of Poisson semigroups associated with the Ornstein--Uhlenbeck, Laguerre and Jacobi operators. We prove that, in the Ornstein--Uhlenbeck and…
We study the subelliptic heat kernels of the CR three dimensional solvable Lie groups. We first classify all left-invariant sub-Riemannian structures on three dimensional solvable Lie groups and obtain representations of these groups. We…
In 1998, V. Liskevich and Y. Semenov showed sharp Gaussian upper bounds for Schr\"odinger semigroups on $\mathbb R^3$ with potentials satisfying a global Kato class condition. Using similar basic ideas we show sharp Gaussian upper bounds…
In this note we investigate the image of Sobolev spaces of fractional order on a compact Lie group $ K $ under the Segal-Bargmann transform. We show that the image can be characterised in terms of certain weighted Bergman spaces of…
We study Chern characters and the assembly mapping for free actions using the framework of geometric $K$-homology. The focus is on the relative groups associated with a group homomorphism $\phi:\Gamma_1\to \Gamma_2$ along with applications…