On Fourier Series Using Functions Other than Sine and Cosine

Authors

Henry Scher, University of MarylandFollow

Abstract

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.

Faculty Sponsor

Lawrence Washington

Recommended Citation

Scher, Henry (2007) "On Fourier Series Using Functions Other than Sine and Cosine," Rose-Hulman Undergraduate Mathematics Journal: Vol. 8: Iss. 2, Article 13.
Available at: https://scholar.rose-hulman.edu/rhumj/vol8/iss2/13