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On local property of absolute summability of factored Fourier series

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arxiv 1301.6874 v1 pith:QC3ATJM6 submitted 2013-01-29 math.AP math.CA

classification math.APmath.CA
keywords summabilityabsolutealphafactoredfourierleftlocalright
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We establish two general theorems on the local properties of the absolute summability of factored Fourier series by applying a recently defined absolute summability, $\left\vert A,\alpha_{n}\right\vert _{k}$ summability, and the class $\mathcal{S}\left( \alpha_{n},\phi_{n}\right) $, which generalize some well known results and can be applied to improve many classical absolute summability methods.

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