Note on weighted qq-Fock spaces and qq-orthogonal polynomials (Mathematical aspects of quantum fields and related topics)

In this short note, we shall discuss weighted $q$-Fock spaces, field operators and their vacuum distributions, which have strong connections with $q$-orthogonal polynomials including discrete $q$-Hermite I polynomials. One can see that our general approach can treat not only known examples scattered in [1][5][8][9][10][13], but also can involve non-trivial and interesting examples, which were not referred in previous works [5][11]. This is a summary paper of our paper [4]

Poisson type operators on the Fock space of type B

The main purpose of this paper is to propose an ( , q)-analogue of the Poisson operators on the Fock space of type B in the sense of Boz˙ ejko, Ejsmont, and Hasebe [J. Funct. Anal. 269, 1769–1795 (2015)] and to find a probability law of this operator. We shall show that the probability law is expressed by the q-Meixner distribution in the sense of Definition 3.2. Our results contain not only symmetric distributions as in Boz˙ ejko-Ejsmont-Hasebe but also the non-symmetric ones such as free Poisson, q and q2-deformations of Poisson, Pascal, Gamma, and Meixner distributions

Characterization of Hida Measures in white noise analysis

The main purpose of this work is to prove Theorem 4.4, so-called, the characterization theorem of Hida measures (generalized measures). As examples of such measures, we shall present the Poisson noise measure and the Grey noise measure in Example 4.5 and 4.6, respectively.Comment: Preprint, July 199