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On the Restricted Cesàro Summability of Multiple Orthogonal Series

Published online by Cambridge University Press:  20 November 2018

Ferenc Móricz
Ferenc Móricz*
Affiliation:
Indiana University, Bloomington, Indiana University of Szeged, Szeged, Hungary
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We actually treat double orthogonal series in detail, simply for the sake of brevity in notations. Multiple orthogonal series will be shortly indicated in the concluding Section 8.

Let (X, , μ) be an arbitrary positive measure space and {ϕjk(x):i, k = 0, 1, …} an orthonormal system defined on X. We consider the double orthogonal series

(1.1)

where {ϕik:i, k = 0, 1, …} is a double sequence of real numbers (coefficients), for which

(1.2)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 2 , 01 April 1985 , pp. 371 - 384
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Alexits, G., Convergence problems of orthogonal series (Pergamon Press, Oxford-New York, 1961).Google Scholar
2. Móricz, F., On the restricted convergence and (C, 1, 1)-summability of double orthogonal series, Acta Sci. Math. (Szeged) (to appear).Google Scholar
3. Móricz, F., On the (C, α ≧ 0, β ≧ 0)-summability of double orthogonal series, Studia Math, (to appear).CrossRefGoogle Scholar
4. Zygmund, A., Sur l'application de la première moyenne arithmétique dans la théorie des séries de fonctions orthogonales, Fund. Math. 10 (1927), 356–362.Google Scholar
5. Zygmund, A., Trigonometric series, Vol I. (University Press, Cambridge, 1959).Google Scholar