On considère un polynôme $P$, à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégrales$${\int }_0^1{\int }_0^1{x}_1^{{\beta }_1-1}{x}_2^{{\beta }_2-1}P(x_1,x_2{)}^{s}d{x}_{1}d{x}_2$$donne des renseignements sur les racines du polynômes de Bernstein de $P$. La détermination des pôles des intégrales peut se faire en utilisant certaines méthodes de Mellin. Des calculs explicites sont donnés.

Let $C_i$ (i = 1,2) be two arbitrary bounded operators on a Banach space. We study (C₁,C₂)-regularized cosine existence and uniqueness families and their relationship to second order abstract Cauchy problems. We also prove some of their basic properties. In addition, Hille-Yosida type sufficient conditions are given for the exponentially bounded case.

In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$-almost periodic functions in ${ℝ}^n,$ slowly oscillating functions in ${ℝ}^n,$ and further analyze the recently introduced class of quasi-asymptotically $c$-almost periodic functions...