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On considère un polynôme $P$ , à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégrales $\int_{0}^{1} \int_{0}^{1} x_{1}^{β_{1} - 1} x_{2}^{β_{2} - 1} P (x_{1}, x_{2})^{s} d x_{1} d x_{2}$ 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.

Reflexivity of convex subsets of L(H) and subspaces of $l^{p}$ .

Shehada, Hasan A. (1991)

International Journal of Mathematics and Mathematical Sciences

Regularized cosine existence and uniqueness families for second order abstract Cauchy problems

Jizhou Zhang (2002)

Studia Mathematica

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.

Remotely $c$ -almost periodic type functions in $ℝ^{n}$

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

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...