. C A ] 3 0 N ov 2 00 1 Integral Transform and Segal - Bargmann Representation associated to q - Charlier Polynomials ∗
نویسنده
چکیده
Let μ (q) p be the q-deformed Poisson measure in the sense of SaitohYoshida [24] and νp be the measure given by Equation (3.6). In this short paper, we introduce the q-deformed analogue of the Segal-Bargmann transform associated with μ (q) p . We prove that our Segal-Bargmann transform is a unitary map of L(μ (q) p ) onto the q-deformed Hardy spaceH (νq). Moreover, we give the Segal-Bargmann representation of the multiplication operator by x in L(μ (q) p ), which is a linear combination of the qcreation, q-annihilation, q-number, and scalar operators.
منابع مشابه
. C A ] 3 S ep 2 00 1 Integral Transform and Segal - Bargmann Representation associated to q - Charlier Polynomials ∗
Let μ (q) p be the q-deformed Poisson measure in the sense of SaitohYoshida [24] and νp be the measure given by Equation (3.6). In this short paper, we introduce the q-deformed analogue of the Segal-Bargmann transform associated with μ (q) p . We prove that our Segal-Bargmann transform is a unitary map of L(μ (q) p ) onto the Hardy space H (νq). Moreover, we give the Segal-Bargmann representati...
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Let μ (q) p be the q-deformed Poisson measure in the sense of SaitohYoshida [24] and νp be the measure given by Equation (3.6). In this short paper, we introduce the q-deformed analogue of the Segal-Bargmann transform associated with μ (q) p . We prove that our Segal-Bargmann transform is a unitary map of L(μ (q) p ) onto the Hardy space H (νq). Moreover, we give the Segal-Bargmann representati...
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