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Certain Groups of Orthonormal Step Functions

  • J. J. Price (a1)

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It was first pointed out by Fine (2), that the Walsh functions are essentially the characters of a certain compact abelian group, namely the countable direct product of groups of order two. Later Chrestenson (1) considered characters of the direct product of cyclic groups of order α (α = 2, 3, …). In general, his results show that the analytic properties of these generalized Walsh functions are basically the same as those of the ordinary Walsh functions.

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References

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1. Chrestenson, H. E., A class of generalized Walsh functions, Pacific J. Math., 5 (1955), 1731.
2. Fine, N. J., On the Walsh functions, Trans. Amer. Math. Soc, 65 (1949), 372414.
3. Ohkuma, T., On a certain system of orthogonal step functions, Tohoku Math. J., 5 (1953), 166177.
4. Vilenkin, N., On a class of complete orthonormal systems, Bull. Acad. Sci. URSS. Ser. Math. (Izvestia Akad. Nauk. SSSR), 11 (1947), 363400 (Russian, English summary).
5. Walsh, J. L., A closed set of normal orthogonal functions, Amer. J. Math., 55 (1923), 524.
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Certain Groups of Orthonormal Step Functions

  • J. J. Price (a1)

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