An important aspect of Fourier series is that sin(x), cos(x) and all of their dilations sin(jx) and cos(jx) for all j create an orthogonal basis of the Hilbert space of periodic square-integrable functions with period 2 p . In this paper, we define the notion of dilation basis and prove that only a pair of orthogonal sinusoidal functions can generate an orthogonal dilation basis of this space.

Author Bio

Henry Scher is from Chevy Chase, Maryland, and is currently enrolled at the University of Maryland, College Park. This paper is a result of research conducted under the guidance of Professor Lawrence Washington.