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A Note on Convergence of Fourier Series of a Function on Wiener's Class Vp

Published online by Cambridge University Press:  20 November 2018

Rafat N. Siddiqi
Rafat N. Siddiqi*
Affiliation:
Department of Physics-Mathematics, Université de Moncton Moncton, N.B., Canada Summer research Institute of Canadian Mathematical Congress Dalhousie University Halifax, N.S., Canada
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Let f be a 2π-periodic function defined on [0, 2π]. We set

where suprema have been taken with respect to all partitions P:a = t0<t1<t2<…<tn<=b of any segment [a, b] contained in [0, 2π]. We call the pth total variation of f on [a, b]. If we denote pth total variaiton of f on [0, 2π] by Vp(f), then we can define Wiener's class simply by

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 243 - 247
Copyright
Copyright © Canadian Mathematical Society 1977

References

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