## Summation of the Fourier Series of Orthogonal Functions |

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absolute convergence absolutely summable allied series assume Bonnet's theorem Bossolasco bounded variation Cesaro summability Chapter complete with respect completes the proof Consequendy continuous function convergence problem converges absolutely converges almost everywhere cosec2 criterion denotes equivalent established evidendy exists fact following theorem follows from Lemma Fourier series function of bounded G. H. Hardy gives Hardy and J. E. Hardy and Litdewood Hardy's theorem Hence hypersphere hypothesis inequality interval of orthogonality J. E. Littlewood K. K. Chen Kogbediantz Laplace series Lebesgue functions Lebesgue's limit lim mean of order Menchoff necessary and sufficient normal orthogonal system normalized orthogonal functions nt dt null-set obtain odd function pn(x positive number proposition prove the following Riesz second theorem sequence series converges series of f(x set of points sufficient condition summable function system of normalized system of orthogonal theorem of mean write Zygmund