Finite-dimensional Calogero representation of the q-differential operator
Abstract
A finite-dimensional matrix representation of the Jackson q-differential operator Dq, defined by Dqf(x) = (f(qx)-f(x))/(x(q-1)), is written down following Calogero. Such a representation of Dq should have applications in q-analysis leading to the corresponding extensions of the numerous results of Calogero's work.
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