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.
Lawrence Washington, Department of Mathematics, University of Marylandlcw@math.umd.edu
"On Fourier Series Using Functions Other than Sine and Cosine,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 8
, Article 13.
Available at: https://scholar.rose-hulman.edu/rhumj/vol8/iss2/13