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Published online by Cambridge University Press: 14 February 2012
An analogue of full-range Fourier series is introduced in the Sturm-Liouville setting and a theorem generalising Wiener's theorem for functions with absolutely convergent Fourier series is proved. The Banach algebra structure of the theory is examined. Use is made of second-order asymptotic formulae for the Sturm-Liouville eigenfunctions.