We investigate Cesaro summability of the Fourier orthogonal expansion of functions on Bd x I m, where Bd is the closed unit ball in Rd and Im is the m-fold Cartesian product of the interval [-1, 1], in terms of orthogonal polynomials with respect to the weight functions (1 - z) alpha(1 + z)beta(1 - |x|2)lambda-1/2 , with z ∈ Im and x ∈ Bd. In addition, we study a discretized Fourier orthogonal expansion on the cylinder B2 x [-1, 1], which uses a finite number of Radon projections. The Lebesgue constant of this operator is obtained, and the proof utilizes generating functions for associated orthogonal series.
Jeremy Wade has a BSc in zoology from Bristol University and a Postgraduate Certificate in Education (PGCE) from the University of Kent. He has worked as a secondary science teacher, a newspaper reporter, and a senior advertising copywriter. He has written for publications including The Times, Guardian, Sunday Telegraph, and BBC Wildlife magazine. His previous book, Somewhere down the Crazy River (with Paul Boote), was published in 1992 to stellar reviews.