The q-Dirac Operator on Quantum Euclidean Space
Abstract
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 Euclidean space that factorizes the Uq(o)-invariant Laplacian q. Due to the non-commutativity of the multiplication, we need a special Clifford algebra C0,nq. We define q-monogenic functions as null solutions of the q-Dirac operator and q-spherical monogenic functions. We define an inner Fischer product and decompose the space of homogeneous polynomials of degree k.
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