An approach to spectral sets of certain zeta-functions

A. Beurling introduced the concept of spectral sets of unbounded functions to study the possibility of the approximation of those by trigonometric polynomials. The author studied spectral sets of the Riemann zeta-function and zeta-functions belonging to a certain class. The purpose of the present paper is to improve the results in the previous studies for spectral sets. The improvement is based on the relation between spectral sets and support of distributions.