Basic Analog of Fourier Series on a q-Linear Grid

✍ Scribed by J. Bustoz; J.L. Cardoso

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 159 KB
• Volume: 112
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.2001.3599

✦ Synopsis

For 0 < q < 1 define the symmetric q-linear operator acting on a suitable function f(x) by df(x)=f(q 1/2 x) -f(q -1/2 x). The q-linear initial value problem df(x) dx = lf(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).