A class of complete orthogonal sequences of broken line functions
Abstract: A class of orthonormal sets of continuous broken line functions is defined. Each member is shown to be complete in and pointwise convergence theorems are obtained for the Fourier expansions relative to these sets.
-  Philip Franklin, A set of continuous orthogonal functions, Math. Ann. 100 (1928), no. 1, 522–529. MR 1512499, https://doi.org/10.1007/BF01448860
-  J. L. Sox Jr. and W. J. Harrington, A class of complete orthogonal sequences of step functions, Trans. Amer. Math. Soc. 157 (1971), 129–135. MR 0275046, https://doi.org/10.1090/S0002-9947-1971-0275046-3
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Keywords: Franklin functions, Fourier series, orthonormal set of functions, complete in , pointwise convergence
Article copyright: © Copyright 1972 American Mathematical Society