Search results for "Daniell integral"

showing 10 items of 15 documents

Kurzweil-Henstock type integral on zero-dimensional group and some of its application

2008

A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.

Abelian integralGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsElementary abelian groupSingular integralLocally compact groupKurzweil-Henstock type integral zero-dimensional groupVolume integralSettore MAT/05 - Analisi MatematicaImproper integralNoncommutative harmonic analysisDaniell integralMathematics
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On Weakly Singular Integral Equations of the Second Kind

1988

Applied MathematicsMathematical analysisComputational MechanicsRiemann integralSingular integralSingular point of a curveIntegral equationVolterra integral equationFourier integral operatorsymbols.namesakeSingular solutionsymbolsDaniell integralMathematicsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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An integral for a banach valued function

2009

Abstract Using partitions of the unity ((PU)-partition), a new definition of an integral is given for a function f : [a, b] → X, where X is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.

Discrete mathematicsBanach valued function (PU)-partition (PU)*-integral Bochner-integralGeneral MathematicsInfinite-dimensional vector functionBochner integralRiemann–Stieltjes integralRiemann integralBochner spaceExponential integralsymbols.namesakeSettore MAT/05 - Analisi MatematicasymbolsPaley–Wiener integralDaniell integralMathematicsTatra Mountains Mathematical Publications
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A Constructive Minimal Integral which Includes Lebesgue Integrable Functions and Derivatives

2000

In this paper we provide a minimal constructive integration process of Riemann type which includes the Lebesgue integral and also integrates the derivatives of differentiable functions. We provide a new solution to the classical problem of recovering a function from its derivative by integration, which, unlike the solution provided by Denjoy, Perron and many others, does not possess the generality which is not needed for this purpose.The descriptive version of the problem was treated by A. M. Bruckner, R. J. Fleissner and J. Foran in [2]. Their approach was based on the trivial observation that for the required minimal integral, a function F is the indefinite integral of f if and only if F'…

Discrete mathematicssymbols.namesakeDifferentiation of integralsGeneral MathematicssymbolsRiemann–Stieltjes integralLocally integrable functionRiemann integralDaniell integralDifferentiable functionLebesgue integrationLebesgue–Stieltjes integrationMathematicsJournal of the London Mathematical Society
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On an iterative method for a class of integral equations of the first kind

1987

In this paper, we investigate an iterative method which has been proposed [1] for the numerical solution of a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right-hand side. Integral equations of this special type occur in experimental physics, astronomy, medical tomography and other fields where density functions cannot be measured directly, but are related to observable functions via integral equations. In order to take into account the non-negativity of density functions, the proposed iterative scheme was defined in such a way that only non-negative solutions can be approximated. The first part o…

DiscretizationIterative methodGeneral MathematicsConvergence (routing)Mathematical analysisGeneral EngineeringFunctional integrationDaniell integralSummation equationIntegral equationMathematicsLocal convergenceComputing and Computers
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Generality of Henstock-Kurzweil type integral on a compact zero-dimensional metric space

2011

ABSTRACT A Henstock-Kurzweil type integral on a compact zero-dimensional metric space is investigated. It is compared with two Perron type integrals. It is also proved that it covers the Lebesgue integral.

General MathematicsInjective metric spaceMathematical analysisLebesgue's number lemmaHenstock-kurzweil integral Perron integral derivation basisRiemann–Stieltjes integralRiemann integralLebesgue integrationVolume integralsymbols.namesakeDifferentiation of integralsSettore MAT/05 - Analisi MatematicasymbolsDaniell integralMathematics
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Henstock type integral in harmonic analysis on zero-dimensional groups

2006

AbstractA Henstock type integral is defined on compact subsets of a locally compact zero-dimensional abelian group. This integral is applied to obtain an inversion formula for the multiplicative integral transform.

Henstock integralApplied MathematicsMathematical analysisLine integralRiemann integralRiemann–Stieltjes integralSingular integralLocally compact groupHenstock–Fourier seriesVolume integralsymbols.namesakeLocally compact zero-dimensional abelian groupImproper integralsymbolsCharacters of a groupInversion formulaDaniell integralMultiplicative integral transformAnalysisMathematicsJournal of Mathematical Analysis and Applications
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A Riemann-Type Integral on a Measure Space

2005

In a compact Hausdorff measure space we define an integral by partitions of the unity and prove that it is nonabsolutely convergent.

Lebesgue measureMathematical analysisMeasure (physics)Mathematics::General Topologypartition of unityRiemann integralRiemann–Stieltjes integralLebesgue integration$PU^*$-integralsymbols.namesakeTransverse measureDifferentiation of integralssymbolsGeometry and TopologyDaniell integral28A25Borel measureAnalysisMathematicsReal Analysis Exchange
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Integral holomorphic functions

2004

We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Frechet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity. In this paper we define and study a class of holomorphic functions over infinite- dimensional Banach spaces admitting integral representation. Our purpose, and the motivation for our definition, are two-fold: we wish to obtain an integral repre- sentation formula …

Mathematics::Functional AnalysisPure mathematicsGeneral MathematicsHolomorphic functional calculusMathematical analysisHolomorphic functionAnalyticity of holomorphic functionsDaniell integralCauchy's integral theoremInfinite-dimensional holomorphyIdentity theoremCauchy's integral formulaMathematicsStudia Mathematica
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Set valued Kurzweil-Henstock-Pettis integral

2005

It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.

Pettis integralKurzweil–Henstock integralMathematics::Functional AnalysisPure mathematicsGeneralizationApplied MathematicsMathematical analysisKurzweil–Henstock–Pettis integralMathematics::Classical Analysis and ODEsRegular polygonselectionRiemann–Stieltjes integralRiemann integralSupport functionLebesgue integrationsupport functionsymbols.namesakemultifunctionPettis set-valued integralsymbolsMathematics::Metric GeometryDaniell integralAnalysisMathematics
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