M. L. Zimmermann

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math.CV2025

$q$ -Fock Space of $q$ -Analytic Functions and its realization in $L^{2} (C; e^{- z z ˉ} d x d y)$

Amedeo Altavilla, Swanhild Bernstein, Martha Lina Zimmermann

We introduce a $q$ -deformation of the Fock space of holomorphic functions on $C$ , based on a geometric definition of $q$ -analyticity. This definition is inspired by a stan…

math.CV2025

Conjugate $(1/ q, q)$ -harmonic Polynomials in $q$ -Clifford Analysis

Swanhild Bernstein, Amedeo Altavilla, Martha Lina Zimmermann

We consider the problem of constructing a conjugate $(1/ q, q)$ -harmonic homogeneous polynomial $V_{k}$ of degree $k$ to a given $(1/ q, q)$ -harmonic homogeneous polynomial $U_{k}$ of de…

math.CV2025

The $q$ -Dirac Operator on Quantum Euclidean Space

Swanhild Bernstein, Martha Lina Zimmermann, Baruch Schneider

This paper provides the foundations of quantum Clifford analysis in $q$ -commutative variables with symmetric difference operators. We consider a $q$ -Dirac operator on the quantum E…

q-Fock Space of q-Analytic Functions and its realization in L2(C;e−zzˉdxdy)

Conjugate (1/q,q)-harmonic Polynomials in q-Clifford Analysis

The q-Dirac Operator on Quantum Euclidean Space

$q$ -Fock Space of $q$ -Analytic Functions and its realization in $L^{2} (C; e^{- z z ˉ} d x d y)$

Conjugate $(1/ q, q)$ -harmonic Polynomials in $q$ -Clifford Analysis

The $q$ -Dirac Operator on Quantum Euclidean Space