We establish Connes’s local trace formula (related to the explicit formulae of number theory) for the quaternions. This is done as an application of a study of the central operator H = log(|x|) + log(|y|) in the context of invariant harmonic analysis. The multiplicative analysis of the additive Fourier transform gives a spectral interpretation to generalized “Tate Gamma functions” (closely akin...

– We analyze from the viewpoint of an abstract Markov operator recent results by D. Nualart and G .Peccati , and I. Nourdin and G. Peccati, on the fourth moment as a condition on a Wiener chaos to have a distribution close to Gaussian. In particular, we are led to introduce a notion of chaos associated to a Markov operator through its iterated gradients and present conditions on the (pure) poin...

We study a quasibound state of a delta -kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths xi of lossy quasibound states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates Gamma are dramatically enhanced. We find the relation xi approximately G...

We compute by means of the Bethe Ansatz the boundary S matrix for the open anisotropic spin-12 chain with diagonal boundary magnetic fields in the noncritical regime (∆ > 1). Our result, which is formulated in terms of q-gamma functions, agrees with the vertex-operator result of Jimbo et al.

The modern study of singular integral operators on curves in the plane began 1970s. Since then, there has been a vast array work done boundedness defined lower dimensional sets Euclidean spaces. In recent years, mathematicians have attempted to push these results into more general metric setting particularly case and graphs Carnot groups. Suppose $$X = Y^*$$ for separable Banach space Y. Any ca...

Functions satisfying a defective renewal equation arise commonly in applied probability models. Usually these functions don’t admit a explicit expression. In this work we consider to approximate them by means of a gamma-type operator given in terms of the Laplace transform of the initial function. We investigate which conditions on the initial parameters of the renewal equation give optimal ord...

The paper describes a novel associative model for the forecasting of time series in petroleum engineering. The model is based on the Gamma classifier, which is inspired on the Alpha-Beta associative memories, taking the alpha and beta operators as basis for the gamma operator. The objective is to reproduce and predict future oil production in different scenarios in an adjustable time window. Th...

We investigate i.i.d. random complex dynamical systems generated by probability measures on finite unions of the loci holomorphic families rational maps Riemann sphere $$\hat{\mathbb {C}}.$$ show that under certain conditions families, for a generic system, (especially, polynomial system,) all but countably many initial values $$z\in \hat{\mathbb {C}}$$ , almost every sequence $$\gamma =(\gamma...

"The goal of this paper is to study the nonexistence nontrivial solutions following Cauchy problem $$\left\{ \begin{array}{ll} u_{tt}+(-\Delta)^{\beta/2} u+u_{t}=\displaystyle\int_{0}^{t}\left(t-\tau \right) ^{-\gamma}\left\vert u(\tau ,\cdot) \right\vert^{p}d\tau,\\ \cr u(0,x)=u_{0}(x),\quad u_t(0,x)=u_1(x),\quad x\in\mathbb{R}^n, \end{array}\right.$$ where $p>1,\ 0<\gamma <1,\,\, \be...