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A Note on the Fourier Coefficients of Unbounded Functions

✍ Scribed by Haslam-Jones, U. S.


Book ID
120101074
Publisher
Oxford University Press
Year
1927
Tongue
English
Weight
95 KB
Volume
s1-2
Category
Article
ISSN
0024-6107

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On the Fourier-Coefficients of Vector-Va
✍ Hermann KΓΆnig πŸ“‚ Article πŸ“… 1991 πŸ› John Wiley and Sons 🌐 English βš– 522 KB

We study the decay of the FOURIER-coefficients of vector-valued functions F :T --+ X, X a BANAFH space. Differentiable functions f generally have absolutely sumrnable FOURIER-coefficients, 1 Ilf(n)ll < 00, iff X is K-convex. More precise statements on the decay of Ilf(n)ll for regular functions fcan