Let X = ε n x n be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable ||X|| in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given. In [6] the second-named author calculated the distribution of a scalar Rademacher series ε n a n...

Let T be the unit circle in the complex plane. Let $/ be the Banach algebra of all complex valued continuous functions on T with absolutely convergent Fourier series. Norbert Wiener [10] proved that if any ƒ in sf is invertible in the ring of continuous functions on T, then \/f also is an element of sf . Paul Levy [7] generalized Wiener's result, showing that for each ƒ in sf and each complex a...