The Journal of the Indian Mathematical Society

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Some Convergence Criteria for Fourier Series


Affiliations
1 Mathematics Department, The Australian National University, Box No. 4, P. O. Canberra, A. C. T, Australia
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Theorem 1. The Fourier series of an even function φ converges to zero at the origin if Φ1(t) = o(t)=o(t) as t → 0 and further if, for any n, there are

m = m(n) > n and m' = m'(n) < n


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  • Some Convergence Criteria for Fourier Series

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Authors

Masako Izumi
Mathematics Department, The Australian National University, Box No. 4, P. O. Canberra, A. C. T, Australia
Shin-ichi Izumi
Mathematics Department, The Australian National University, Box No. 4, P. O. Canberra, A. C. T, Australia

Abstract


Theorem 1. The Fourier series of an even function φ converges to zero at the origin if Φ1(t) = o(t)=o(t) as t → 0 and further if, for any n, there are

m = m(n) > n and m' = m'(n) < n