Electronic Resource
Springer
Periodica mathematica Hungarica
13 (1982), S. 71-74
ISSN:
1588-2829
Keywords:
Primary 42A56
;
Walsh functions
;
dyadic derivatives
;
Rademacher functions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We show that in order for a Walsh series to be locally constant it is necessary for certain blocks of that series to sum to zero. As a consequence, we show that a functionf with a somewhat sparse Walsh—Fourier series is necessarily a Walsh polynomial if its strong dyadic derivative is constant on an interval. In particular, if a Rademacher seriesR is strongly dyadically differentiable and if that derivative is constant on any open subset of [0, 1], thenR is a Rademacher polynomial.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01848097
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