I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis representation should be reasonably smooth (physically, the spectral function represents the density of states).
I have tried using the Gaussian function with varying widths, but it seems to lack the continuity to represent a physical quantity (too many oscillations). Orthogonal polynomials (eg.Legendre) could work, but those basis functions are not non-negative, so I was wondering if anyone has ideas on representing this spectral function with an ideal, or at least reasonable, basis other than the Gaussian basis.
Thank you all.