Abstract
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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