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Absolute Nevanlinna Summability and Fourier Series

โœ Scribed by G.D. Dikshit

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
160 KB
Volume
248
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

We adopt here an extended version of the absolute Nevanlinna summability and apply it to study Fourier series of functions of bounded variations. The absolute < < Riesz summability R, n, โฅ , โฅ G 0, which is equivalent to the absolute Cesaro < < summability C, โฅ , is obtainable from the Nevanlinna summability. As such from the theorems proved here we deduce some results on the absolute Cesaro summa-bility of Fourier series. Some of these results are new while some others improve upon known theorems. แฎŠ 2000 Academic Press โฆ < < R, n, โฅ , โฅ ) 0, which is known to be equivalent to the Cesaro-method < < < ลฝ .< C, โฅ . Results proved for the method N q may thus relate to the results โฆ on absolute Cesaro summability.

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