Basic Analog of Fourier Series on a q-Linear Grid

Authors: Bustoz J.¹; Cardoso J.L.²

Source: Journal of Approximation Theory, Volume 112, Number 1, September 2001 , pp. 134-157(24)

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Abstract:

For 0<q<1 define the symmetric q-linear operator acting on a suitable function f(x) by f(x)=f(q^1/2x)-f(q^-1/2x). The q-linear initial value problem f(x)x= f(x),f(0)=1, has two entire functions C_q(z) and S_q(z) as linearly independent solutions. The functions C_q(z) and S_q(z) are orthogonal on a discrete set. We consider Fourier expansions in these functions and derive analytic bounds on the roots of S_q(z). Copyright 2001 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, Arizona State University, Tempe, Arizona, 85287-1804 2: Department of Mathematics, Universidade de Tras-Os-Montes e Alto Douro, Vila Real, Portugal

Publication date: 2001-09-01