Search results for "Continuous polynomials"

showing 2 items of 2 documents

Factorization of absolutely continuous polynomials

2013

In this paper we study the ideal of dominated (p,s)-continuous polynomials, that extend the nowadays well known ideal of p-dominated polynomials to the more general setting of the interpolated ideals of polynomials. We give the polynomial version of Pietsch s factorization Theorem for this new ideal. Our factorization theorem requires new techniques inspired in the theory of Banach lattices.

Discrete mathematicsMathematics::Commutative AlgebraPietsch's domination theoremApplied MathematicsDiscrete orthogonal polynomialsClassical orthogonal polynomialsMacdonald polynomialsDifference polynomialsAbsolutely continuous polynomialsFactorization of polynomialsHahn polynomialsWilson polynomialsOrthogonal polynomialsMATEMATICA APLICADAAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Zeroes of real polynomials on C(K) spaces

2007

AbstractFor a compact Hausdorff topological space K, we show that the function space C(K) must satisfy the following dichotomy: (i) either it admits a positive definite continuous 2-homogeneous real-valued polynomial, (ii) or every continuous 2-homogeneous real-valued polynomial vanishes in a non-separable closed linear subspace. Moreover, if K does not have the Countable Chain Condition, then every continuous polynomial, not necessarily homogeneous and with arbitrary degree, has constant value in an isometric copy of c0(Γ), for some uncountable Γ.

PolynomialFunction spaceApplied MathematicsC(K) spacesMathematical analysisHausdorff spaceContinuous polynomialsLinear subspaceZero-setSquare-free polynomialCombinatoricsCompact spaceCountable chain conditionHomogeneous polynomialAnalysisMathematicsJournal of Mathematical Analysis and Applications
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