Abstract

It= ~ ~(k)wk(x) k--0 be a Walsh series and `4 a certain class of Walsh series. When E is a subset of the dyadic group, it is called a set of uniqueness for ,4, if tt E A and 2n--I lim E ft(k)wk(x) = 0 everywhere except on E k=O imply tha t ft(k) = 0 for k = 0, 1,2, . . . . When E is not a set of uniqueness for `4, it is called a set of multiplicity for ,4. It is easy to see tha t a subset of the dyadic group is a set of uniqueness for the class of all Walsh series It such tha t

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