Search results for "classical"

showing 10 items of 2294 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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Finitely randomized dyadic systems and BMO on metric measure spaces

2015

Abstract We study the connection between BMO and dyadic BMO in metric measure spaces using finitely randomized dyadic systems, and give a Garnett–Jones type proof for a theorem of Uchiyama on a construction of certain BMO functions. We obtain a relation between the BMO norm of a suitable expectation over dyadic systems and the dyadic BMO norms of the original functions in different systems. The expectation is taken over only finitely randomized dyadic systems to overcome certain measurability questions. Applying our result, we derive Uchiyama’s theorem from its dyadic counterpart, which we also prove.

Discrete mathematicsMathematics::Functional AnalysisDyadic cubeApplied Mathematicsta111Mathematics::Analysis of PDEsMathematics::Classical Analysis and ODEsMetric measure spaceBounded mean oscillationQuantitative Biology::OtherBounded mean oscillationRandomized dyadic systemMetric spaceNorm (mathematics)Dyadic BMOAnalysisMathematicsNonlinear Analysis: Theory, Methods & Applications
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A multilinear Phelps' Lemma

2007

We prove a multilinear version of Phelps' Lemma: if the zero sets of multilinear forms of norm one are 'close', then so are the multilinear forms.

Discrete mathematicsMathematics::Functional AnalysisLemma (mathematics)CeroMultilinear mapbiologyApplied MathematicsGeneral MathematicsMathematics::Classical Analysis and ODEsComputer Science::Computational Complexitybiology.organism_classificationCombinatoricsNorm (mathematics)MathematicsProceedings of the American Mathematical Society
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Factorization of (q,p)-summing polynomials through Lorentz spaces

2017

[EN] We present a vector valued duality between factorable (q,p)-summing polynomials and (q,p)-summing linear operators on symmetric tensor products of Banach spaces. Several applications are provided. First, we prove a polynomial characterization of cotype of Banach spaces. We also give a variant of Pisier's factorization through Lorentz spaces of factorable (q,p)-summing polynomials from C(K)-spaces. Finally, we show a coincidence result for (q,p)-concave polynomials.(c) 2016 Elsevier Inc. All rights reserved.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApplied MathematicsDiscrete orthogonal polynomials010102 general mathematicsBanach space010103 numerical & computational mathematics01 natural sciencesClassical orthogonal polynomialsDifference polynomialsFactorizationPisier's theoremWilson polynomialsOrthogonal polynomialsSymmetric tensorSumming polynomialsFactorization0101 mathematicsMATEMATICA APLICADAAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Domination spaces and factorization of linear and multilinear summing operators

2015

[EN] It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutely p-summing linear operators, (p, sigma)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p(1), ... , p(n))-dominated multilinear operators and dominated (p(1), ... , p(n); sigma)-continuous multilinear operators.

Discrete mathematicsMultilinear mapPietsch's domination theoremMultilinear summing operators010102 general mathematicsMathematics::Classical Analysis and ODEs010103 numerical & computational mathematicsPietsch's domination theorem factorization of operators multilinear summing operators.Factorization of operators01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisMathematics (miscellaneous)FactorizationFOS: Mathematics0101 mathematicsMATEMATICA APLICADAMathematics
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A note on projective coordinate systems of modular lattices

1993

This note clarifies the combinatorial nature of projective coordinate systems of modular upper continuous lattices. It generalizes the classical relationship between 3-dimensional Desarguesian configurations and coordinate systems of projective 3-spaces.

Discrete mathematicsPure mathematicsClassical modular curveBlocking setDuality (projective geometry)Projective spaceGeometry and TopologyEllipsoidal coordinatesCoordinate spacePencil (mathematics)Twisted cubicMathematicsJournal of Geometry
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A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

Discrete mathematicsPure mathematicsIntegrable systemMathematics::General MathematicsLogicMathematics::Classical Analysis and ODEsFunction (mathematics)Fuzzy logicComputingMethodologies_PATTERNRECOGNITIONArtificial IntelligenceIf and only ifSettore MAT/05 - Analisi MatematicaFuzzy Henstock integral fuzzy McShane integral Henstock-Kurzweil and McShane equiintegrabilityFuzzy numberLocally integrable functionComputingMethodologies_GENERALMathematicsDecomposition theorem
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Haar Type and Carleson Constants

2009

For a collection ℰ of dyadic intervals, a Banach space X, and p∈(1, 2], we assume the upper l p estimates where x I ∈X, and h I denotes the L ∞ normalized Haar function supported on I. We determine the minimal requirement on the size of ℰ such that these estimates imply that X is of Haar type p. The characterization is given in terms of the Carleson constant of ℰ.

Discrete mathematicsPure mathematicsMathematics::Functional AnalysisGeneral MathematicsBanach spaceMathematics::Classical Analysis and ODEsHaarFunction (mathematics)Characterization (mathematics)Type (model theory)Functional Analysis (math.FA)Mathematics - Functional Analysis46B20FOS: Mathematics46B07Constant (mathematics)46B07 ; 46B20Mathematics
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The Action of the Symplectic Group Associated with a Quadratic Extension of Fields

1999

Abstract Given a quadratic extension L/K of fields and a regular alternating space (V, f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group SpL(V, f) in the set of K-subspaces of V.

Discrete mathematicsPure mathematicsSymplectic groupAlgebra and Number TheoryGroup (mathematics)Symplectic representationSymplectic vector spaceQuadratic equationDimension (vector space)Metaplectic groupSettore MAT/03 - GeometriaMoment mapMathematicsGeometry of classical groups Canonical forms reduction classificationJournal of Algebra
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Probabilistic Interpretations of Predicates

2016

In classical logic, any m-ary predicate is interpreted as an m-argument two-valued relation defined on a non-empty universe. In probability theory, m-ary predicates are interpreted as probability measures on the mth power of a probability space. m-ary probabilistic predicates are equivalently semantically characterized as m-dimensional cumulative distribution functions defined on \(\mathbb {R}^m\). The paper is mainly concerned with probabilistic interpretations of unary predicates in the algebra of cumulative distribution functions defined on \(\mathbb {R}\). This algebra, enriched with two constants, forms a bounded De Morgan algebra. Two logical systems based on the algebra of cumulative…

Discrete mathematicsUnary operationComputer Science::Logic in Computer ScienceCumulative distribution functionClassical logicProbabilistic logicRandom variableŁukasiewicz logicDe Morgan algebraMathematicsProbability measure
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