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A Fourier Formula for Series Summable (C, 1)

Published online by Cambridge University Press:  20 November 2018

George Cross
George Cross*
Affiliation:
University of Waterloo
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Recently Bullen (1) developed a J3-integral that gives a Fourier representation for trigonometric series when both the series and its conjugate are summable (C, 1) everywhere. Earlier Cross (4) had shown that the C2P-integral (3) was strong enough to integrate such series and, indeed, that any trigonometric series for which the series and its conjugate were summable (C, k) were Fourier series where the integral used in the formula for the coefficients was the Ck+iP-integral (3). In (1) Bullen defines a J4-integral and says, without proof, that a Fourier formula in terms of this integral may be obtained for series for which the series and its conjugate are summable (C, 2) and the coefficients o(n).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 27 - 32
Copyright
Copyright © Canadian Mathematical Society 1966

References

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