On the Computer Characterization of Seabeds by Sonars

Spectral geometry, homogeneous spaces and differential forms with finite Fourier series

“…If p = 0 and if M = S 1 , then this yields, modulo a slight change of notation, the classical Fourier series decomposition f (θ) = n a n e inθ and a function has a finite Fourier series on the circle if and only if it is a trigonometric polynomial. There is an extensive literature on the subject with appropriate physical applications, several representative items being [2,3,7,8,18].…”