Search results for " EXTENSION"

showing 10 items of 272 documents

Linear extension operators on products of compact spaces

2003

Abstract Let X and Y be the Alexandroff compactifications of the locally compact spaces X and Y , respectively. Denote by Σ( X × Y ) the space of all linear extension operators from C(( X × Y )⧹(X×Y)) to C(( X × Y )) . We prove that X and Y are σ -compact spaces if and only if there exists a T∈Σ( X × Y ) with ‖ T ‖ Γ∈Σ( X × Y ) with ‖ Γ ‖=1. Assuming the existence of a T∈Σ( X × Y ) with ‖ T ‖ X and Y is equivalent to the fact that ‖ Γ ‖⩾2 for every Γ∈Σ( X × Y ) .

Pure mathematicsAlexandroff compactificationLinear extensionMathematical analysisLinear extension operatorProduct topologyGeometry and TopologyLocally compact spaceProduct spaceSpace (mathematics)MathematicsTopology and its Applications
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Multiplicities of fields of values of irreducible characters of finite groups

2021

We show that if f f is the largest multiplicity of the fields of values of the irreducible characters of a finite group G G , then | G | |G| is bounded from above in terms of f f .

Pure mathematicsApplied MathematicsGeneral MathematicsGalois extensionMathematicsProceedings of the American Mathematical Society
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Fibred-categorical obstruction theory

2022

Abstract We set up a fibred categorical theory of obstruction and classification of morphisms that specialises to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further applications are provided to crossed extensions and crossed bimodule butterflies, with in particular a classification of non-abelian extensions of unital associative algebras in terms of Hochschild cohomology.

Pure mathematicsFibrationCohomology Fibration Category of fractions Schreier-Mac Lane theorem Obstruction theory Crossed extension Hochschild cohomologyFibered knotMathematics::Algebraic TopologyCohomologyHochschild cohomologyMorphismMathematics::K-Theory and HomologyMathematics::Category TheoryCategorical variableMathematicsSchreier-Mac Lane theoremAlgebra and Number TheoryFunctorCategory of fractionsGroup (mathematics)Crossed extensionSettore MAT/01 - Logica MatematicaObstruction theoryCohomologyCategory of fractions; Cohomology; Crossed extension; Fibration; Hochschild cohomology; Obstruction theory; Schreier-Mac Lane theoremSettore MAT/02 - AlgebraBimoduleObstruction theory
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Algebraic time-reversal operation

1999

International audience; We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) U(4) K(4) = A(4) ^ S(4) S(4) Td. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators.

Pure mathematicsFunction field of an algebraic variety[ PHYS.QPHY ] Physics [physics]/Quantum Physics [quant-ph]010304 chemical physics03.65.Fd Algebraic methods - 31.15.Hz Group theoryAlgebraic extensionDimension of an algebraic variety010402 general chemistry01 natural sciencesAtomic and Molecular Physics and Optics0104 chemical sciencesAlgebraic cycle[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]Algebraic methodsQuantum mechanics0103 physical sciencesAlgebraic surfaceReal algebraic geometryAlgebraic functionGroup theoryDifferential algebraic geometryMathematicsThe European Physical Journal D
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Weighted estimates for diffeomorphic extensions of homeomorphisms

2019

Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\varphi$ and of $\varphi^{-1} .$

Pure mathematicsMathematics::Functional AnalysisMathematics - Complex VariablesdiffeomorphismGeneral MathematicsMultiple integralHigh Energy Physics::Phenomenologyinternal chord-arc domainPoisson extensionExtension (predicate logic)OmegafunktioteoriaHomeomorphism (graph theory)Domain (ring theory)FOS: MathematicsDiffeomorphismComplex Variables (math.CV)Mathematics
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Approximation by uniform domains in doubling quasiconvex metric spaces

2020

We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.

Pure mathematicsPrimary 30L99. Secondary 46E35 26B30Algebraic geometry01 natural sciencesDomain (mathematical analysis)funktioteoriaQuasiconvex functionMathematics::Group TheoryquasiconvexityMathematics - Metric Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsuniform domainComputer Science::DatabasesMathematicsPartial differential equationFunctional analysis010102 general mathematicsMetric Geometry (math.MG)General Medicinemetriset avaruudetMetric spaceBounded functionSobolev extension010307 mathematical physicsfunktionaalianalyysi
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Sobolev Extension on Lp-quasidisks

2021

AbstractIn this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of classical quasidisks. After that, we also find some applications of this property.

Pure mathematicsSobolev extension domainsProperty (philosophy)Lp-quasidisksMathematics::Complex Variables010102 general mathematicsMathematics::Analysis of PDEs0102 computer and information sciencesExtension (predicate logic)01 natural sciencesPotential theoryfunktioteoriaSobolev spacehomeomorphism of finite distortion010201 computation theory & mathematics0101 mathematicsfunktionaalianalyysiAnalysisMathematicsPotential Analysis
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Fibered aspects of Yoneda's regular span

2018

In this paper we start by pointing out that Yoneda's notion of a regular span $S \colon \mathcal{X} \to \mathcal{A} \times \mathcal{B}$ can be interpreted as a special kind of morphism, that we call fiberwise opfibration, in the 2-category $\mathsf{Fib}(\mathcal{A})$. We study the relationship between these notions and those of internal opfibration and two-sided fibration. This fibrational point of view makes it possible to interpret Yoneda's Classification Theorem given in his 1960 paper as the result of a canonical factorization, and to extend it to a non-symmetric situation, where the fibration given by the product projection $Pr_0 \colon \mathcal{A} \times \mathcal{B} \to \mathcal{A}$ i…

Pure mathematicsSpan (category theory)FibrationAlgebraic structureGeneral MathematicsCohomology; Crossed extension; Fibration; Regular spanFibered knot01 natural sciencesCohomologyMorphismMathematics::Category Theory0103 physical sciencesFOS: MathematicsClassification theoremCategory Theory (math.CT)0101 mathematicsMathematicsCrossed extension010102 general mathematicsFibrationMathematics - Category TheoryMathematics - Rings and AlgebrasSettore MAT/02 - AlgebraTransfer (group theory)Regular spanRings and Algebras (math.RA)Product (mathematics)010307 mathematical physics
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Some spectral mapping theorems through local spectral theory

2004

The spectral mapping theorems for Browder spectrum and for semi-Browder spectra have been proved by several authors [14], [29] and [33], by using different methods. We shall employ a local spectral argument to establish these spectral mapping theorems, as well as, the spectral mapping theorem relative to some other classical spectra. We also prove that ifT orT* has the single-valued extension property some of the more important spectra originating from Fredholm theory coincide. This result is extended, always in the caseT orT* has the single valued extension property, tof(T), wheref is an analytic function defined on an open disc containing the spectrum ofT. In the last part we improve a re…

Pure mathematicsSpectral theoryTransform theoryGeneral MathematicsSpectrum (functional analysis)Mathematical analysisExtension (predicate logic)Single valued extension property Weyl and semi-Browder operators spectral mapping theorems Weyl’s theoremFredholm theorySpectral linesymbols.namesakesymbolsSpectral theory of ordinary differential equationsAnalytic functionMathematicsRendiconti del Circolo Matematico di Palermo
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A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting

2015

Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.

Pure mathematicsWeak convergenceRiesz representation theoremRiesz potential(D)-convergenceGeneral MathematicsD-convergenceMathematical analysisMathematics::Classical Analysis and ODEsHilbert spaceRiesz spaceRiesz spaceKurzweil-Henstock integralRiesz space order convergence D-convergence Kurzweil-Henstock integral Hake theoremHake theoremsymbols.namesakeRiesz–Fischer theoremM. Riesz extension theoremorder convergencesymbolsMathematics (all)Riesz–Thorin theoremMathematics
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