Construction of the generalised q-derivative operators
Dayanand Parashar and Deepak Parashar
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Submission date: 12. Jul. 2001
published in: Journal of geometry and physics, 48 (2003) 2-3, p. 297-308
DOI number (of the published article): 10.1016/S0393-0440(03)00045-7
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear operator which is multiplicative over functions of a real variable. The validity of the general prescriptions is ascertained by considering suitable examples of such derivatives and constructing their eigenfunctions explicitly. The relationship of a particular version of the operator with the one-dimensional Möbius transformation is also established.