论文标题
近似理论的尖锐常数。 V.与给定的牛顿多面体有关的渐近平等
Sharp Constants of Approximation Theory. V. An Asymptotic Equality Related to Polynomials with Given Newton Polyhedra
论文作者
论文摘要
令$ v \ subset \ r^m $为一个凸体，对所有坐标超重平面，让$ \ pp_ {av}，\，\ ge 0 $为所有代数多条件的一组，其牛顿polyhedra为$ av $ $ av $。我们证明，限制平等是$ a \ to \ iy $之间的多项式多项式的多变量Markov-Bernstein-Nikolskii类型不平等，从$ \ pp_ {av} $与$ v $ speptrum in Spectrum in $ v $的Explumenty类型的整个功能的相应常数。
Let $V\subset\R^m$ be a convex body, symmetric about all coordinate hyperplanes, and let $\PP_{aV},\, a\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subsets of $aV$. We prove a limit equality as $a\to \iy$ between the sharp constant in the multivariate Markov-Bernstein-Nikolskii type inequalities for polynomials from $\PP_{aV}$ and the corresponding constant for entire functions of exponential type with the spectrum in $V$.
