Radial Bargmann representation for the Fock space of type B

Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \cite{BEH15} as the distribution of the $(\alpha,q)$-Gaussian process (the Gaussian process of type B) over the $(\alpha,q)$-Fock space (the Fock space of type B). The main purpose of this paper is to find the radial Bargmann representation of $\nu_{\alpha,q}$. Our main results cover not only the representation of $q$-Gaussian distribution by \cite{LM95}, but also of $q^2$-Gaussian and symmetric free Meixner distributions on $\mathbb R$. In addition, non-trivial commutation relations satisfied by $(\alpha,q)$-operators are presented.Comment: 13 pages, minor changes have been mad

Semigroups of distributions with linear Jacobi parameters

We show that a convolution semigroup of measures has Jacobi parameters polynomial in the convolution parameter $t$ if and only if the measures come from the Meixner class. Moreover, we prove the parallel result, in a more explicit way, for the free convolution and the free Meixner class. We then construct the class of measures satisfying the same property for the two-state free convolution. This class of two-state free convolution semigroups has not been considered explicitly before. We show that it also has Meixner-type properties. Specifically, it contains the analogs of the normal, Poisson, and binomial distributions, has a Laha-Lukacs-type characterization, and is related to the $q=0$ case of quadratic harnesses.Comment: v3: the article is merged back together with arXiv:1003.4025. A significant revision following suggestions by the referee. 2 pdf figure

Contactless Electroreflectance Study of Temperature Dependence of Fundamental Band Gap of ZnSe

We report a systematic study of the temperature variation of the energy [E$\text{}_{0}$(T)] and broadening parameter [Γ$\text{}_{0}$(T)] of the fundamental band gap of ZnSe in the range 27 K < T < 370 K using contactless electroreflectance. The obtained values of E$\text{}_{0}$(T) and Γ$\text{}_{0}$(T) have been fit to various semi-empirical expressions to obtain information about the exciton-phonon coupling in this system. The experimentally determined E$\text{}_{0}$(T) also is of significance for technological applications since it can be used to determine the operating temperature of ZnSe-based devices such as quantum well lasers

Interpretation of Urban Surface Models using 2D Building Information

While aiming on a task like 3D building reconstruction the interpretation process can be simplified if Digital Surface Models (DSM), which can either be derived by stereo matching from aerial images or be directly measured by scanning laser systems are used additionally to or instead of image data. Images contain much information, but just this complexity causes enormous problems for the automatic interpretation of this data type. Since the information of a DSM is restricted to surface geometry its interpretation is simplified by the absence of unnecessary details