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- W2945953756 abstract "For two polynomials of degrees $n$ and $m$ ($ngeq m$) $$ fleft( sright) =a_{0}+a_{1}s+ldots+a_{n-1}s^{n-1}+a_{n}s^{n}$$ and $$gleft( sright) =b_{0}+b_{1}s+ldots+b_{m-1}s^{m-1}+b_{m}s^{m}$$ we define a set of polynomials $fbullet g =left{ F_{0},ldots,F_{n-m}right} $, where [ F_{j}left( sright) =a_{j}b_{0}+a_{j+1}b_{1}s+ldots+a_{j+m}b_{m}s^{m}, ] for $j=0,ldots,n-m$, and call it textit{a generalized Hadamard product of $f$ and $g$}. We give sufficient conditions for the Hurwitz stability of $fbullet g$. The obtained results show that the famous Garloff--Wagner theorem on the Hurwitz stability of the Hadamard product of polynomials is a special case of a more general fact. We also show that for every polynomial with positive coefficients (even not necessarily stable) one can find a polynomial such that their generalized Hadamard product is stable. Some connections with polynomials admitting the Hadamard factorization are also given. Numerical examples complete and illustrate the considerations." @default.
- W2945953756 created "2019-05-29" @default.
- W2945953756 creator A5055966882 @default.
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- W2945953756 date "2019-05-17" @default.
- W2945953756 modified "2023-10-01" @default.
- W2945953756 title "The generalized Hadamard product of polynomials and its stability" @default.
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