## Absolute Summability of Fourier Series and Orthogonal Series |

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absolute convergence absolute Nörlund summability An(t Analysis ancos Applications assumptions Banach Spaces behaviour belongs best approximation bounded variation Chapter condition consider constant converges Corollary defined denote depends easily Edited equivalent establish estimate everywhere exists extend finite following theorem Fourier series function Further given hand Hence hold hypothesis immediate implies increasing sequence integrable interval Izumi known Lemma Let f(x Let pn log(n+1 Math monotone decreasing sequence nºn non-decreasing function non-increasing non-negative and non-increasing obtain Okuyama orthogonal series periodic positive positive numbers positive sequence Proceedings Proof of Theorem proved the following respectively satisfying series of f(x similarly summability of Fourier summability R,Pnell summable N,Pnl Suppose Theorem 8.6 Theory trigonometric VII VII virtue write