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BIRS Workshop Lecture Videos

Relations between polynomial solutions, extensions, radical ideals and Lipschitz normal embeddings. Michalska, Maria


Take polynomials $f,g\in k[X]$, where $k$ is the field of complex or real numbers. Under certain assumptions we show equivalence of the following conditions: (i) $(f,g)$ is radical (ii) for every polynomial $h$ if there exists a pointwise solution of $$ A\cdot f + B\cdot g =h $$ then there exists its polynomial solution (iii) every continuous function $$ F=\left\{\begin{array}{ll} \alpha & on\ \{f=0\}\\ \beta & on\ \{g=0\} \end{array}\right. $$ with $\alpha,\beta\in{k}[X]$, is a restriction of a polynomial. We will discuss relation of (i-iii) with Lipschitz normal embeddings. Work in progress.

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