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Summary  

A. Beurling introduced the concept of spectral sets of unbounded functions to study the possibility of the approximation of those by trigonometric polynomials. We consider spectral sets of unbounded functions in a certain class which contains the square of the Riemann zeta-function as a typical example.

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Abstract  

A. Beurling introduced harmonic functions attached to measurable functions satisfying suitable conditions and defined their spectral sets. The concept of spectral sets is closely related to approximations by trigonometric polynomials. In this paper we consider spectral sets of the harmonic functions attached to the Riemann zeta-function and its modification.

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