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A Structure Theorem for the Absolute RIESZ Summability of FOURIER Series

✍ Scribed by B. D. Malviya

Publisher
John Wiley and Sons
Year
1972
Tongue
English
Weight
292 KB
Volume
54
Category
Article
ISSN
0025-584X

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✦ Synopsis

of Denton (Texas) (Eingegangen am 4.6. 1971)

1. Definitions

Let a, be a giveninfinite series and let A, = il (n) be a positive inonotonic function of n tending t o infinity with n. We write

The series z c n , i s said to he summable (R, An, r ) , r 2 0, t o sum s, if A > ( w ) / w ' --+ s, as OJ 00, and is said to be absolutely summuble (R, A$%, r ) or summable IR, A,,, r 1, r 2 0 if A;(w),'cu' is of bounded variation in ( A , m ) ,

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