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Uniform convergence and everywhere convergence of Fourier series. II

Published online by Cambridge University Press:  17 April 2009

Masako Izumi  and
Shin-ichi Izumi
Masako Izumi
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
Shin-ichi Izumi
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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The first theorem shows that the subspaces of the space of functions with everywhere convergent Fourier series, defined in our previous paper, is a good subspace. The second theorem shows that convergence criterion in the previous paper is the proper generalization of Lebesgue's Convergence Criterion.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 3 , December 1973 , pp. 337 - 342
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Gergen, J.J., “Convergence and summability criteria for Fourier series”, Quart. J. Math. Oxford 1 (1930), 252–275.CrossRefGoogle Scholar
[2]Izumi, Masako and Izumi, Shin-ichi, “Uniform convergence and everywhere convergence of Fourier series. I”, Bull. Austral. Math. Soc. 9 (1973), 321–335.CrossRefGoogle Scholar