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On a System of Step Functions

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Abstract

It is well known that the Riemann hypothesis is equivalent to the following statement: the identity function belongs to the linear span in L 2(0,1) of the family

$$\left[ {\frac{\alpha }{x}} \right] - \alpha \left[ {\frac{1}{x}} \right],{\text{ 0}} < \alpha < {\text{1}}{\text{.}}$$

A step is presented in describing the set of all idempotents representable as a finite sum of functions of the form (*). Bibliography: 10 titles.

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, Russia

    V. I. Vasyunin

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  1. V. I. Vasyunin
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Vasyunin, V.I. On a System of Step Functions. Journal of Mathematical Sciences 110, 2930–2943 (2002). https://doi.org/10.1023/A:1015331119128

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