An alternative approach to a theorem of Tom Meurman
R. Balasubramanian, K. Ramachandra (1990)
Acta Arithmetica
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R. Balasubramanian, K. Ramachandra (1990)
Acta Arithmetica
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Enrico Bombieri (1971)
Acta Arithmetica
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Kurt Mahler, G. Szekeres (1967)
Acta Arithmetica
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K. Chandrasekharan, H. Joris (1973)
Acta Arithmetica
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Jeffrey Vaaler (1981)
Acta Arithmetica
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J. Proschan (1971)
Acta Arithmetica
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Eugene Levine, Joseph O'Sullivan (1977)
Acta Arithmetica
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B. Srinivasan (1963)
Acta Arithmetica
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Chang-Pao Chen (1994)
Studia Mathematica
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We prove that if as max(|j|,|k|) → ∞, and , then f(x,y)ϕ(x)ψ(y) ∈ L¹(T²) and as min(m,n) → ∞, where f(x,y) is the limiting function of the rectangular partial sums , (ϕ,θ) and (ψ,ϑ) are pairs of type I. A generalization of this result concerning L¹-convergence is also established. Extensions of these results to double series of orthogonal functions are also considered. These results can be extended to n-dimensional case. The aforementioned results generalize work of Balashov [1],...