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Saturation results for a class of linear operators

Published online by Cambridge University Press:  24 October 2008

B. Kuttner ,
R. N. Mohapatra  and
B. N. Sahney
B. Kuttner
Affiliation:
University of Birmingham
R. N. Mohapatra
Affiliation:
University of Birmingham
B. N. Sahney
Affiliation:
American University of Beirut
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Let B denote the space of bounded measurable functions with period 2π. We will suppose throughout that f(x) ∈ B. All norms considered are essential sup norms. Let the Fourier series of f(x) be given by

Let D = (dnk) (n, k = 0, 1, …) be an infinite matrix.

Let Ln(f; x) be the D transform of the Fourier series of f(t) at t = x, i.e.

where Sk(x) = A0(x) + A1(x) + … + Ak(x). Let us write

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 1 , July 1983 , pp. 133 - 148
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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