A class of complete orthogonal sequences of step functions
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- by J. L. Sox and W. J. Harrington PDF
- Trans. Amer. Math. Soc. 157 (1971), 129-135 Request permission
Abstract:
A class of orthogonal sets of step functions is defined and each member is shown to be complete in ${L_2}(0,1)$. Pointwise convergence theorems are obtained for the Fourier expansions relative to these sets. The classical Haar orthogonal set is shown to be a set of this class and the class itself is seen to be a subclass of the “generalized Haar systems” defined recently by Price.References
- Philip Franklin, A set of continuous orthogonal functions, Math. Ann. 100 (1928), no. 1, 522–529. MR 1512499, DOI 10.1007/BF01448860
- Alfred Haar, Zur Theorie der orthogonalen Funktionensysteme, Math. Ann. 69 (1910), no. 3, 331–371 (German). MR 1511592, DOI 10.1007/BF01456326
- J. J. Price, An algebraic characterization of certain orthonormal systems, Proc. Amer. Math. Soc. 19 (1968), 268–273. MR 225085, DOI 10.1090/S0002-9939-1968-0225085-9
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 157 (1971), 129-135
- MSC: Primary 42.15
- DOI: https://doi.org/10.1090/S0002-9947-1971-0275046-3
- MathSciNet review: 0275046