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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

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