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The approximate symmetric integral

1989
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Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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By a symmetric integral is understood an integral obtained from some kind of symmetric derivation process. Such integrals arise most naturally in the study of trigonometric series and in particular to handle the following problem. Suppose that a trigonometric series (1) AQ/2 + ^ cik cos kx + bk sin kx k=\ converges everywhere to a function/. It is known that this may occur without / being integrable in any of the more familiar senses so that the series may not be considered as a Fourier series

doi:10.4153/cjm-1989-023-8
fatcat:5so35ibp7vaxfdmx5y5nxt4t5y