Investigation of the properties of functions in the space \(N_{\Phi}\) depending on the geometry of their spectrum. (Q1432385)

In the present paper, certain properties of entire functions of exponential type that belong, as functions of a real variable, to the space \(N_{\Phi}\) of all Lebesgue measurable functions \(f:\mathbb R ^{n}\to \mathbb C\) such that \(\int_{0}^{\infty}\Phi(\lambda_{f}(t)) \,dt<\infty,\) where \(\Phi\) is a positive concave function on \([0,\infty),\) are examined. No proofs are given.