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Papers by Antal Veres

Research paper thumbnail of Absolute convergence of double Walsh–Fourier series and related results

Acta Mathematica Hungarica, 2011

We consider the double Walsh orthonormal system {wm(x)wn(y) : m, n ∈ N} * Corresponding author.

Research paper thumbnail of On the absolute convergence of multiple fourier series

Acta Mathematica Hungarica, 2007

Let f : R N → C be a periodic function with period 2π in each variable. We prove sucient conditio... more Let f : R N → C be a periodic function with period 2π in each variable. We prove sucient conditions for the absolute convergence of the multiple Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to multiple Fourier series.

Research paper thumbnail of Absolute convergence of multiple Fourier series revisited

Absolute convergence of multiple Fourier series revisited

Analysis Mathematica, 2008

In a recent paper [4], Gogoladze and Meskhia generalized the classical results of Bernstein, Szás... more In a recent paper [4], Gogoladze and Meskhia generalized the classical results of Bernstein, Szász, Zygmund and others related to absolute convergence of single trigonometric Fourier series. Our aim is to extend these results from single to multiple Fourier series. To this effect, we introduce the notions of multiplicative moduli of continuity and that of smoothness. Multiplicative Lipschitz classes of

Research paper thumbnail of Absolute convergence of double Walsh–Fourier series and related results

Acta Mathematica Hungarica, 2011

We consider the double Walsh orthonormal system {wm(x)wn(y) : m, n ∈ N} * Corresponding author.

Research paper thumbnail of On the absolute convergence of multiple fourier series

Acta Mathematica Hungarica, 2007

Let f : R N → C be a periodic function with period 2π in each variable. We prove sucient conditio... more Let f : R N → C be a periodic function with period 2π in each variable. We prove sucient conditions for the absolute convergence of the multiple Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to multiple Fourier series.

Research paper thumbnail of Absolute convergence of multiple Fourier series revisited

Absolute convergence of multiple Fourier series revisited

Analysis Mathematica, 2008

In a recent paper [4], Gogoladze and Meskhia generalized the classical results of Bernstein, Szás... more In a recent paper [4], Gogoladze and Meskhia generalized the classical results of Bernstein, Szász, Zygmund and others related to absolute convergence of single trigonometric Fourier series. Our aim is to extend these results from single to multiple Fourier series. To this effect, we introduce the notions of multiplicative moduli of continuity and that of smoothness. Multiplicative Lipschitz classes of

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