A differentiation theorem for functions defined on the dyadic rationals
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- by R. J. Lindahl PDF
- Proc. Amer. Math. Soc. 30 (1971), 349-352 Request permission
Abstract:
In this paper we show that under certain conditions a real-valued function defined on an interval of dyadic rational numbers is a monotone function. One of these conditions involves a generalized differentiability property. From this result we offer a new proof of a conjecture of N. Fine concerning the uniqueness of solution of Walsh series.References
- Richard B. Crittenden and Victor L. Shapiro, Sets of uniqueness on the group $2^{\omega }$, Ann. of Math. (2) 81 (1965), 550–564. MR 179535, DOI 10.2307/1970401
- N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372–414. MR 32833, DOI 10.1090/S0002-9947-1949-0032833-2 S. Saks, Théorie de l’intégrale, Monografie Mat., vol. 2, PWN, Warsaw, 1933; English transl., Monografie Mat., vol. 7, PWN, Warsaw; Hafner, New York, 1937.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 349-352
- MSC: Primary 26.40; Secondary 42.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0284549-2
- MathSciNet review: 0284549