Basic Analog of Fourier Series on a q-Linear Grid


AbstractFor 0<q<1 define the symmetric q-linear operator acting on a suitable function f (x) by δf(x)=f(q1/2x)−f(q−1/2x). The q-linear initial value problem δf(x)δx= λf (x),f(0)=1, has two entire functions Cq(z) and Sq(z) as linearly independent solutions. The functions Cq(z) and Sq(z) are orthogonal on a discrete set. We consider Fourier expansions in these functions and derive analytic bounds on the roots of Sq(z)

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Last time updated on 6/5/2019

This paper was published in Elsevier - Publisher Connector .

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