Some properties of the double spectral function for dual amplitude with mandelstam analyticity $\operatorname{Re}\alpha(s)\eqslantless\operatorname{const}$

A study is made of the asymptotic behavior of the dual amplitude with Mandelstam analyticity in the region of the double spectral function. It is shown that if the trajectory of a Regge pole is bounded by the condition $\operatorname{Re}\alpha(s)\eqslantless\operatorname{const}$as $s\to\infty$, the amplitude satisfies a Mandelstare representation with finitely many subtractions. The double spectral function takes its greatest value in strips along its boundaries.