Matches in SemOpenAlex for { <https://semopenalex.org/work/W2111000125> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W2111000125 abstract "The moment problem for compact semi-algebraic sets has been solved in [S1] (see [PD], Section 6.4, for a refinement of the result). In the terminology explained below, this means that each defining sequence f of a compact semialgebraic set Kf has property (SMP ). On the other hand, for many noncompact semi-algebraic sets (for instance, sets containing a cone of dimension two [KM], [PS]) the moment problem is not solvable. Only very few noncompact semi-algebraic sets (classes of real algebraic curves [So], [KM], [PS] and cylinder sets [Mc]) are known to have a positive solution of the moment problem. In this paper we study semi-algebraic setsKf such that there exist polynomials h1, . . ., hn which are bounded on the set Kf . Our main result (Theorem 1) reduces the moment problem for the set Kf to the moment problem for the “fiber sets” Kf ∩Cλ, where Cλ is real algebraic variety {x ∈ R : h1(x) = λ1, . . ., hn(x) = λn}. From this theorem new classes of non-compact closed semi-algebraic sets are obtained for which the moment problem has an affirmative solution. Combined with a result of V. Powers and C. Scheiderer [PS], it follows that tube sets around certain real algebraic curves have property (SMP ) (see Theorem 9). Let f = (f1, . . ., fk) be a finite set of polynomials fj ∈ R[x] ≡ R[x1, . . ., xd] and let K ≡ Kf be the associated closed semi-algebraic subset defined by" @default.
- W2111000125 created "2016-06-24" @default.
- W2111000125 creator A5045417574 @default.
- W2111000125 date "2003-01-20" @default.
- W2111000125 modified "2023-09-27" @default.
- W2111000125 title "On the moment problem of closed semi-algebraic sets" @default.
- W2111000125 cites W1483432773 @default.
- W2111000125 cites W1577431998 @default.
- W2111000125 cites W1968222759 @default.
- W2111000125 cites W1980857824 @default.
- W2111000125 cites W2006555769 @default.
- W2111000125 cites W2085352155 @default.
- W2111000125 cites W2088660795 @default.
- W2111000125 cites W2097743263 @default.
- W2111000125 cites W2150788398 @default.
- W2111000125 cites W2313382788 @default.
- W2111000125 cites W2481849377 @default.
- W2111000125 cites W4244999758 @default.
- W2111000125 cites W4254742099 @default.
- W2111000125 cites W4255442211 @default.
- W2111000125 doi "https://doi.org/10.1515/crll.2003.040" @default.
- W2111000125 hasPublicationYear "2003" @default.
- W2111000125 type Work @default.
- W2111000125 sameAs 2111000125 @default.
- W2111000125 citedByCount "28" @default.
- W2111000125 countsByYear W21110001252013 @default.
- W2111000125 countsByYear W21110001252014 @default.
- W2111000125 countsByYear W21110001252015 @default.
- W2111000125 countsByYear W21110001252016 @default.
- W2111000125 countsByYear W21110001252019 @default.
- W2111000125 crossrefType "journal-article" @default.
- W2111000125 hasAuthorship W2111000125A5045417574 @default.
- W2111000125 hasBestOaLocation W21110001252 @default.
- W2111000125 hasConcept C105795698 @default.
- W2111000125 hasConcept C121332964 @default.
- W2111000125 hasConcept C134306372 @default.
- W2111000125 hasConcept C136119220 @default.
- W2111000125 hasConcept C179254644 @default.
- W2111000125 hasConcept C199343813 @default.
- W2111000125 hasConcept C202444582 @default.
- W2111000125 hasConcept C2777686260 @default.
- W2111000125 hasConcept C28826006 @default.
- W2111000125 hasConcept C33923547 @default.
- W2111000125 hasConcept C4285052 @default.
- W2111000125 hasConcept C71924100 @default.
- W2111000125 hasConcept C74650414 @default.
- W2111000125 hasConcept C9376300 @default.
- W2111000125 hasConcept C9679016 @default.
- W2111000125 hasConceptScore W2111000125C105795698 @default.
- W2111000125 hasConceptScore W2111000125C121332964 @default.
- W2111000125 hasConceptScore W2111000125C134306372 @default.
- W2111000125 hasConceptScore W2111000125C136119220 @default.
- W2111000125 hasConceptScore W2111000125C179254644 @default.
- W2111000125 hasConceptScore W2111000125C199343813 @default.
- W2111000125 hasConceptScore W2111000125C202444582 @default.
- W2111000125 hasConceptScore W2111000125C2777686260 @default.
- W2111000125 hasConceptScore W2111000125C28826006 @default.
- W2111000125 hasConceptScore W2111000125C33923547 @default.
- W2111000125 hasConceptScore W2111000125C4285052 @default.
- W2111000125 hasConceptScore W2111000125C71924100 @default.
- W2111000125 hasConceptScore W2111000125C74650414 @default.
- W2111000125 hasConceptScore W2111000125C9376300 @default.
- W2111000125 hasConceptScore W2111000125C9679016 @default.
- W2111000125 hasIssue "558" @default.
- W2111000125 hasLocation W21110001251 @default.
- W2111000125 hasLocation W21110001252 @default.
- W2111000125 hasOpenAccess W2111000125 @default.
- W2111000125 hasPrimaryLocation W21110001251 @default.
- W2111000125 hasRelatedWork W2041614387 @default.
- W2111000125 hasRelatedWork W2076564641 @default.
- W2111000125 hasRelatedWork W2078240805 @default.
- W2111000125 hasRelatedWork W2263470246 @default.
- W2111000125 hasRelatedWork W2286484118 @default.
- W2111000125 hasRelatedWork W2885964212 @default.
- W2111000125 hasRelatedWork W2963499202 @default.
- W2111000125 hasRelatedWork W3099593009 @default.
- W2111000125 hasRelatedWork W4297086829 @default.
- W2111000125 hasRelatedWork W99708544 @default.
- W2111000125 hasVolume "2003" @default.
- W2111000125 isParatext "false" @default.
- W2111000125 isRetracted "false" @default.
- W2111000125 magId "2111000125" @default.
- W2111000125 workType "article" @default.