On convergence of Fourier series of functions of generalized bounded variation
Daniel Waterman (1972)
Studia Mathematica
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Displaying similar documents to “On the Fourier series of functions of bounded Φ-variation”
On convergence of Fourier series of functions of generalized bounded variation
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Since the trigonometric Fourier series of an integrable function does not necessarily converge to the function in the mean, several additional conditions have been devised to guarantee the convergence. For instance, sufficient conditions can be constructed by using the Fourier coefficients or the integral modulus of the corresponding function. In this paper we give a Hardy-Karamata type Tauberian condition on the Fourier coefficients and prove that it implies the convergence of the Fourier...
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In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in -norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by we mean , the collection of uniformly W-continuous functions f(x, y), endowed...