A unified approach to uniqueness of Walsh series and Haar series
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- by William R. Wade PDF
- Proc. Amer. Math. Soc. 99 (1987), 61-65 Request permission
Abstract:
We obtain a uniqueness theorem for Walsh series valid for subsequences of ${2^n}$th partial sums which satisfy a pointwise growth condition.References
- G. Alexits, Convergence problems of orthogonal series, International Series of Monographs in Pure and Applied Mathematics, Vol. 20, Pergamon Press, New York-Oxford-Paris, 1961. Translated from the German by I. FΓΆlder. MR 0218827
- F. G. Arutjunjan and A. A. Talaljan, Uniqueness of series in Haar and Walsh systems, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1391β1408 (Russian). MR 0172056
- Richard B. Crittenden and Victor L. Shapiro, Sets of uniqueness on the group $2^{\omega }$, Ann. of Math. (2) 81 (1965), 550β564. MR 179535, DOI 10.2307/1970401
- N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372β414. MR 32833, DOI 10.1090/S0002-9947-1949-0032833-2
- R. J. Lindahl, A differentiation theorem for functions defined on the dyadic rationals, Proc. Amer. Math. Soc. 30 (1971), 349β352. MR 284549, DOI 10.1090/S0002-9939-1971-0284549-2
- V. A. Skvorcov, Haar series with convergent subsequences of partial sums, Dokl. Akad. Nauk SSSR 183 (1968), 784β786 (Russian). MR 0246041
- William R. Wade, A uniqueness theorem for Haar and Walsh series, Trans. Amer. Math. Soc. 141 (1969), 187β194. MR 243265, DOI 10.1090/S0002-9947-1969-0243265-9
- William R. Wade and Kaoru Yoneda, Uniqueness and quasimeasures on the group of integers of a $p$-series field, Proc. Amer. Math. Soc. 84 (1982), no.Β 2, 202β206. MR 637169, DOI 10.1090/S0002-9939-1982-0637169-9
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 61-65
- MSC: Primary 42C25; Secondary 42C10, 43A75
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866430-2
- MathSciNet review: 866430