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Prog. Theor. Phys. Supplement No.150 (2003) pp. 401-410
Analytic Properties of a Special q-Exponential Function
Andreas Ruffing and
Moritz Simon
Munich University of Technology, Dept. of Mathematics,
Boltzmannstraße 3, D-85747 Garching, Germany
Abstract:
(Δq f)(z):= (f(qz)-f
(q-1z)) / (qz-q-1z), \forallz ∈\BbbC \setminus{0}
yields for q ∈(0,1) the so-called symmetric q-difference operator on
\BbbC \setminus{0}. Holomorphic solutions to the fixed point problem
of this q-difference operator and of Δq2 are
elaborated. The analytic properties of the corresponding holomorphic
functions are investigated. A link between the eigenfunctions and the
q-Fourier transform by Koornwinder and Swarttouw on a q-linear grid
is established. The relevance of the fixed point problem to discrete
Schrödinger theory is briefly mentioned.
URL :
http://ptp.ipap.jp/link?PTPS/150/401/
DOI : 10.1143/PTPS.150.401
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