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- W132284364 abstract "It is known that the elementary symmetric polynomials $e_k(x)$ have the property that if $ x, y in [0,infty)^n$ and $e_k(x) leq e_k(y)$ for all $k$, then $||x||_p leq ||y||_p$ for all real $0leq p leq 1$, and moreover $||x||_p geq ||y||_p$ for $1leq p leq 2$ provided $||x||_1 =||y||_1$. Previously the author proved this kind of property for $p>2$, for certain polynomials $F_{k,r}(x)$ which generalize the $e_k(x)$. In this paper we give two additional generalizations of this type, involving two other families of polynomials. When $x$ consists of the eigenvalues of a matrix $A$, we give a formula for the polynomials in terms of the entries of $A$, generalizing sums of principal $k times k$ subdeterminants." @default.
- W132284364 created "2016-06-24" @default.
- W132284364 creator A5091032966 @default.
- W132284364 date "2013-02-19" @default.
- W132284364 modified "2023-09-27" @default.
- W132284364 title "More symmetric polynomials related to p-norms" @default.
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