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Fejér means for multivariate Fourier series. (English) Zbl 0904.42009
The authors prove an analogue to Fejér’s classical theorem in multivariate $$l-1$$ summability. Their attractive result reads as follows: In $$l-1$$ summability the Cesàro $$(C,2d- 1)$$ means of the Fourier series of a function $$f$$ in $$C(\mathbb{T}^d)$$ converge uniformly to $$f$$. In particular, the means define a positive linear polynomial approximate identity on $$C(\mathbb{T}^d)$$; the order of summability is best possible in the sense that the $$(C,\delta)$$ means are not positive for $$0<\delta< 2d-1$$.
They also discuss the Abel means.

##### MSC:
 42B08 Summability in several variables
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