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Uniqueness of Almost Everywhere Convergent Vilenkin Series |
Canad. Math. Bull. 47(2004), 475-480
Published:2004-09-01
Printed: Sep 2004
Printed: Sep 2004
- W. R. Wade
Abstract
D. J. Grubb [3] has shown that uniqueness holds, under a
mild growth condition, for Vilenkin series which converge almost
everywhere to zero. We show that, under even less restrictive
growth conditions, one can replace the limit function 0 by an
arbitrary $f\in L^q$, when $q>1$.
| MSC Classifications: |
43A75 - Analysis on specific compact groups 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |