Statistical convergence of multiple sequences |
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Authors: | F Móricz |
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Institution: | (1) Bolyai Institute, University of Szeged, Aradi Vértanúk Tere 1, 6720 Szeged, Hungary |
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Abstract: | We extend the concept of and basic results on statistical convergence from
ordinary (single) sequences to multiple sequences of (real or complex) numbers.
As an application to Fourier analysis, we obtain the following Theorem 3: (i)
If $f \in L(\textrm{log}^{+} L)^{d-1}(\mathbb{T}^d)$, where $\mathbb{T}^d := -\pi, \pi)^{d}$
is the d-dimensional torus, then the Fourier
series of f is statistically convergent to $f({\bf t})$
at almost every ${\bf t} \in \mathbb{T}^d$; (ii) If $f \in C(\mathbb{T}^d)$, then the
Fourier series of f
is statistically convergent to $f ({\bf t})$ uniformly on $\mathbb{T}^d$.
Received: 5 November 2001 |
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Keywords: | Primary 40A05 40B05 Secondary 42B05 |
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