scholarly journals On the spherical summability of multiple orthogonal series

1951 ◽  
Vol 71 (1) ◽  
pp. 136-136 ◽  
Author(s):  
Josephine Mitchell
Keyword(s):  
Orthogonal Series ◽  
Multiple Orthogonal Series

On the Restricted Cesàro Summability of Multiple Orthogonal Series

1985 ◽  
Vol 37 (2) ◽  
pp. 371-384
Author(s):  
Ferenc Móricz
Keyword(s):  
Measure Space ◽  
Positive Measure ◽  
Orthogonal Series ◽  
Orthonormal System ◽  
Double Sequence ◽  
Real Numbers ◽  
Section 8 ◽  
Double Orthogonal Series ◽  
Multiple Orthogonal Series ◽  
Image Position

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)

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