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Summation Formulas for the product of the q-Kummer Functions from
H. Ahmedov, I. H. Duru
Using the representation of E_q(2) on the non-commutative space zz^*-qz^*z=σ; q<1, σ>0 summation formulas for the product of two, three and four q-Kummer functions are derived.
Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra
H. Ahmedov, I. H. Duru
SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the grou…
Unitary representations of the 2-dimensional Euclidean group in the Heisenberg algebra
H. Ahmedov, I. H. Duru
E(2) is studied as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the unitary irreducible representations of the gr…
Green function on the quantum plane
H. Ahmedov, I. H. Duru
Green function (which can be called the q-analogous of the Hankel function) on the quantum plane E_q^2= E_q(2)/U(1) is constructed.