On the summation of the Fourier series
Vikramaditya Singh (1980)
Mathematica Slovaca
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Displaying similar documents to “On a generalization of Fourier series”
On the summation of the Fourier series
Convergence of generalized conjugate partial sums of Fourier series.
Per Sjölin (2004)
Collectanea Mathematica
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Generalized conjugate partial sums of Fourier series are used to find jumps of functions. The rate of convergence is studied and sharp results are obtained.
Cyclic overlattices, II (Diophantine approximation and sums of roots of unity)
A. Jones (1971)
Acta Arithmetica
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A generalization of Atkinson's formula to L-functions
Tom Meurman (1986)
Acta Arithmetica
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Some new convergence criteria for Fourier series
Godfrey Harold Hardy, John Edensor Littlewood (1934)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Weighted integrability and L¹-convergence of multiple trigonometric series
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],...