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تسجيل مستخدم جديدSmooth Selection for Infinite Sets
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Whitneys extension problem asks the following: Given a compact set $Esubsetmathbb{R}^n$ and a function $f:Eto mathbb{R}$, how can we tell whether there exists $Fin C^m(mathbb{R}^n)$ such that $F|_E=f$? A 2006 theorem of Charles Fefferman answers this question in its full generality. In this paper, we establish a version of this theorem adapted for variants of the Whitney extension problem, including nonnegative extensions and the smooth selection problems. Among other things, we generalize the results of Fefferman-Israel-Luli (2016) to the setting of infinite sets.
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String-averaging is an algorithmic structure used when handling a family of operators in situations where the algorithm at hand requires to employ the operators in a specific order. Sequential orderings are well-known and a simultaneous order means t
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Let $X$ be an infinite dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exists a constant $lambda>0$ and an infinite sequence $(x_i)_{i=1}^inftysubset X$ such that $|x_i-x_j|=lambda$ for all $i eq j$.
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Entrywise functions preserving the cone of positive semidefinite matrices have been studied by many authors, most notably by Schoenberg [Duke Math. J. 9, 1942] and Rudin [Duke Math. J. 26, 1959]. Following their work, it is well-known that entrywise
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