5 papers · 1 filter
-Fock Space of -Analytic Functions and its realization in
Amedeo Altavilla, Swanhild Bernstein, Martha Lina Zimmermann
We introduce a -deformation of the Fock space of holomorphic functions on , based on a geometric definition of -analyticity. This definition is inspired by a stan…
The -Dirac Operator on Quantum Euclidean Space
Swanhild Bernstein, Martha Lina Zimmermann, Baruch Schneider
This paper provides the foundations of quantum Clifford analysis in -commutative variables with symmetric difference operators. We consider a -Dirac operator on the quantum E…
Conjugate -harmonic Polynomials in -Clifford Analysis
Swanhild Bernstein, Amedeo Altavilla, Martha Lina Zimmermann
We consider the problem of constructing a conjugate -harmonic homogeneous polynomial of degree to a given -harmonic homogeneous polynomial of de…
Paley-Wiener Type Theorems associated to Dirac Operators of Riesz-Feller type
Swanhild Bernstein, Nelson Faustino
This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathb…
Hardy decomposition of higher order Lipschitz classes by polymonogenic functions
Lianet De la Cruz Toranzo, Ricardo Abreu Blaya, Swanhild Bernstein
In this paper we find a decomposition of higher order Lipschitz functions into the traces of a polymonogenic function and solve a related Riemann-Hilbert problem. Our approach lies…