Matches in SemOpenAlex for { <https://semopenalex.org/work/W1480820863> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W1480820863 abstract "The classical Remez inequality bounds the maximum of the absolute value of a polynomial $P(x)$ of degree $d$ on $[-1,1]$ through the maximum of its absolute value on any subset $Z$ of positive measure in $[-1,1]$. It was shown in cite{Yom3} that the Lebesgue measure in the Remez inequality can be replaced by a certain geometric invariant $omega_d(Z)$ which can be effectively estimated in terms of the metric entropy of $Z$ and which may be nonzero for discrete and even finite sets $Z$. In the present paper we first obtain an essentially sharp Remez-type inequality in the spirit of cite{Yom3} for complex polynomials of one variable, introducing metric invariants $c_d(Z)$ and $o_{cd}(Z)$ for an arbitrary subset $Zsubset D_1subset {mathbb C}$. These invariants translate into the the metric language the classical Cartan lemma (see cite{Gor} and references therein). Next we introduce $(s,p)$-valent functions, which provide a natural generalization of $p$-valent ones (see cite{Hay} and references therein). We prove a distortion theorem for such functions, comparing them with polynomials sharing their zeroes. On this base we extend to $(s,p)$-valent functions our polynomial Remez-type inequality. As the main example we consider restrictions $g$ of polynomials of a growing degree to a fixed algebraic curve, for which we obtain an essentially sharp local Remez-type inequality, stressing the role of the geometry of singularities of $g$. Finally, we obtain for such functions $g$ a global Remez-type inequality which is valid for all the branches of $g$ and involves both the geometry of singularities of $g$ and its monodromy." @default.
- W1480820863 created "2016-06-24" @default.
- W1480820863 creator A5052491254 @default.
- W1480820863 date "2011-02-13" @default.
- W1480820863 modified "2023-09-27" @default.
- W1480820863 title "Generalized Remez Inequality for $(s,p)$-Valent Functions" @default.
- W1480820863 cites W2016952115 @default.
- W1480820863 cites W2046807088 @default.
- W1480820863 cites W2051691117 @default.
- W1480820863 cites W2072218949 @default.
- W1480820863 cites W2083925726 @default.
- W1480820863 cites W2506126720 @default.
- W1480820863 cites W2583867411 @default.
- W1480820863 hasPublicationYear "2011" @default.
- W1480820863 type Work @default.
- W1480820863 sameAs 1480820863 @default.
- W1480820863 citedByCount "1" @default.
- W1480820863 countsByYear W14808208632014 @default.
- W1480820863 crossrefType "posted-content" @default.
- W1480820863 hasAuthorship W1480820863A5052491254 @default.
- W1480820863 hasConcept C114614502 @default.
- W1480820863 hasConcept C118615104 @default.
- W1480820863 hasConcept C134306372 @default.
- W1480820863 hasConcept C18903297 @default.
- W1480820863 hasConcept C2777299769 @default.
- W1480820863 hasConcept C2777759810 @default.
- W1480820863 hasConcept C33923547 @default.
- W1480820863 hasConcept C46757340 @default.
- W1480820863 hasConcept C86803240 @default.
- W1480820863 hasConcept C90119067 @default.
- W1480820863 hasConceptScore W1480820863C114614502 @default.
- W1480820863 hasConceptScore W1480820863C118615104 @default.
- W1480820863 hasConceptScore W1480820863C134306372 @default.
- W1480820863 hasConceptScore W1480820863C18903297 @default.
- W1480820863 hasConceptScore W1480820863C2777299769 @default.
- W1480820863 hasConceptScore W1480820863C2777759810 @default.
- W1480820863 hasConceptScore W1480820863C33923547 @default.
- W1480820863 hasConceptScore W1480820863C46757340 @default.
- W1480820863 hasConceptScore W1480820863C86803240 @default.
- W1480820863 hasConceptScore W1480820863C90119067 @default.
- W1480820863 hasLocation W14808208631 @default.
- W1480820863 hasOpenAccess W1480820863 @default.
- W1480820863 hasPrimaryLocation W14808208631 @default.
- W1480820863 hasRelatedWork W1541730833 @default.
- W1480820863 hasRelatedWork W1595423872 @default.
- W1480820863 hasRelatedWork W1614153987 @default.
- W1480820863 hasRelatedWork W1978794151 @default.
- W1480820863 hasRelatedWork W1982869314 @default.
- W1480820863 hasRelatedWork W2016215847 @default.
- W1480820863 hasRelatedWork W2024190829 @default.
- W1480820863 hasRelatedWork W2024669050 @default.
- W1480820863 hasRelatedWork W2044740967 @default.
- W1480820863 hasRelatedWork W2056056133 @default.
- W1480820863 hasRelatedWork W2084992011 @default.
- W1480820863 hasRelatedWork W2332628759 @default.
- W1480820863 hasRelatedWork W2607104212 @default.
- W1480820863 hasRelatedWork W2781609394 @default.
- W1480820863 hasRelatedWork W279495 @default.
- W1480820863 hasRelatedWork W2949715239 @default.
- W1480820863 hasRelatedWork W2951934604 @default.
- W1480820863 hasRelatedWork W2951998002 @default.
- W1480820863 hasRelatedWork W3025606763 @default.
- W1480820863 hasRelatedWork W3194637193 @default.
- W1480820863 isParatext "false" @default.
- W1480820863 isRetracted "false" @default.
- W1480820863 magId "1480820863" @default.
- W1480820863 workType "article" @default.