Search results for "Real analysis"

showing 5 items of 5 documents

The Classical Theory of Real Functions

1998

The first class of real functions we deal with in this chapter is the class of functions of locally finite variation. These functions are closely related to the real measures on B. Exploiting this connection would allow us to obtain the properties of these functions from the general results in Chapter 4. But the path we follow here is a more direct one which applies the theory of vector lattices. The link with the measures on B will be established in the next section.

AlgebraClass (set theory)Real analysisComputer scienceSimple functionPath (graph theory)Link (knot theory)Classical limitFirst classConnection (mathematics)
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On the inductive inference of recursive real-valued functions

1999

AbstractWe combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functions of recursive real numbers. In each case we find natural examples of learnable classes of functions and unlearnable classes of functions.

Complex-valued functionGeneral Computer ScienceReal analysisLearning theoryComputable numberInductive inference0102 computer and information sciences02 engineering and technology01 natural sciencesμ-recursive functionComputable analysisTheoretical Computer ScienceAlgebraμ operatorComputable functionReal-valued computationReal-valued function010201 computation theory & mathematics0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingAlgorithmComputer Science(all)MathematicsTheoretical Computer Science
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ON THE FUNDAMENTAL THEOREM OF CALCULUS FOR FRACTAL SETS

2015

The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock–Kurzweil type is introduced.

Differentiation under the integral signReal analysisFundamental theoremApplied Mathematicss-SetMathematics::Classical Analysis and ODEss-HK IntegralDifferential calculusTime-scale calculusIntegration by substitutionAlgebraSettore MAT/05 - Analisi MatematicaModeling and SimulationFundamental theorem of calculusFunctions Hs-ACGδ.CalculusGeometry and TopologyGradient theoremMathematicsFractals
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Leonida Tonelli: A Biography

2011

This paper aims at going through the work by Leonida Tonelli, with a focus on the results he got in the fields of Real Analysis and Calculus of Variations, and put it within the socio-political context of his time. One of the most outstanding Italian analysts in the first half of twentieth century, first in Bologna and then in Pisa and Rome, Leonida Tonelli’s path combined elements of different, conflictual in some moment, relationships which featured at that time Italian mathematics and which linked the latter with Giovanni Gentile, the Fascism and the after-war “new”Italy.

LiteratureReal analysisbusiness.industrymedia_common.quotation_subjectBiographyContext (language use)ArtbusinessClassicsmedia_common
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Higher Order Sobolev-Type Spaces on the Real Line

2014

This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.

PointwiseMathematics::Functional AnalysisArticle SubjectReal analysislcsh:Mathematicsta111Mathematical analysisMathematics::Analysis of PDEsFinite differencelcsh:QA1-939Sobolev inequalitySobolev spaceInterpolation spaceSobolev functionsBirnbaum–Orlicz spaceReal lineAnalysisMathematicsJournal of Function Spaces
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