Let {φ n } be a sequence of continuous functions orthogonal on an interval with respect to a positive measure da, and let h(n) -(\ \φ n \ z da\ . Then under hypotheses general enough to include as special cases the trigonometric system {e inx } 9 the ultraspherical polynomials, and most cases of the Jacobi polynomials, the sequences <α> satisfying || a ||=Σ~=o I a(n) I h(n)< oo form a Banach algebra with a convolution defined by <α*δ> = where Σ;=o c (n)h(n)φ n = (2£-o a(n)h(ri)φ n )(Σn=o

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... )φ n ). Attention is centered upon sequences <α> of unit norm (called distribution sequences), and the associated orthogonal serieŝ Σιd{n)h{n)φ n (called characteristic functions). Theorems on divisibility and stability of these classes are proved, the results being modeled after the corresponding ones about the class of characteristic functions in probability theory.