Search results for "extension theorem"

showing 6 items of 6 documents

A theorem of insertion and extension of functions for normal spaces

1993

Discrete mathematicsPure mathematicsArzelà–Ascoli theoremIsomorphism extension theoremFréchet spaceGeneral MathematicsClosed graph theoremRiesz–Thorin theoremOpen mapping theorem (functional analysis)Brouwer fixed-point theoremMathematicsCarlson's theoremArchiv der Mathematik
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The Riesz Representation Theorem and Extension of Vector Valued Additive Measures

2001

Discrete mathematicsPure mathematicsM. Riesz extension theoremRiesz representation theoremKelvin–Stokes theoremRiesz potentialApplied MathematicsBanach spaceExtension (predicate logic)Characterization (mathematics)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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Quadratic variation of martingales in Riesz spaces

2014

We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ http://dx.doi.org/10.1016/j.jmaa.2013.08.037 National Research Foundation of South Africa (Grant specific unique reference number (UID) 85672) and by GNAMPA of Italy (U 2012/000574 20/07/2012 and U 2012/000388 09/05/2012)

Discrete mathematicsPure mathematicsRiesz potentialRiesz representation theoremApplied MathematicsmartingaleRiesz spaceRiesz spacevector latticeQuadratic variationquadratic variationM. Riesz extension theoremSettore MAT/05 - Analisi MatematicaAustin’s theorem Martingale Measure-free stochastic processes Quadratic variation Riesz space Vector latticemeasure-free stochastic processesAustinʼs theoremMartingale (probability theory)AnalysisMathematics
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Integration of functions ranging in complex Riesz space and some applications in harmonic analysis

2015

The theory of Henstock—Kurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.

Henstock integralSeries (mathematics)Riesz representation theoremRiesz potentialintegral transformGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsHilbert spacegroup characterRiesz spacezero-dimensional compact Abelian groupcharacterHenstock—Kurzweil integralComplex Riesz space character Henstock integral basis integral transform.Riesz transformsymbols.namesakeFourier transformM. Riesz extension theorembasissymbolsMathematics (all)complex Riesz spaceMathematicsMathematical Notes
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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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Topics in calculus and geometry on metric spaces

2022

In this thesis we present an overview of some important known facts related to topology, geometry and calculus on metric spaces. We discuss the well known problem of the existence of a lipschitz equivalent metric to a given quasiultrametric, revisiting known results and counterexamples and providing some new theorems, in an unified approach. Also, in the general setting of a quasi-metric doubling space, suitable partition of unity lemmas allows us to obtain, in step two Carnot groups, the well known Whitney’s extension theorem for a given real function of class C^m defined on a closed subset of the whole space: this result relies on relevant properties of the symmetrized Taylor’s polynomial…

quasi-ultrametric spacecalculuCarnot groupconvexityLipschitz functionmetric spaceWhitney type extension theoremextension theoremdoubling spacepartitionSettore MAT/05 - Analisi Matematicasemi-distance distancepaces of homogeneous typequasi-metric spacesmetrization theoremof unity lemma
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