Search results for "Perron integral"

showing 4 items of 4 documents

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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Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series

2015

Abstract The problem of recovering the coefficients of rectangular convergent multiple Haar and Walsh series from their sums, by generalized Fourier formulas, is reduced to the one of recovering a function (the primitive) from its derivative with respect to the appropriate derivation basis. Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals are compared and it is shown that a Perron-type integral, defined by major and minor functions having a special continuity property, solves the coefficients problem for series which are convergent everywhere outside some uniqueness sets.

Pure mathematicsBasis (linear algebra)Series (mathematics)Applied MathematicsMathematical analysisMathematics::Classical Analysis and ODEsHaarFunction (mathematics)Type (model theory)HAar and Walsh seriesKurzweil-Henstock integral Perron integralsymbols.namesakeFourier transformSettore MAT/05 - Analisi MatematicaWalsh functionsymbolsUniquenessAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Comparison of the P-integral with Burkill's integrals and some applications to trigonometric series

2023

It is proved that the $P_r$-integral [9] which recovers a function from its derivative defined in the space $L^r$, 1 ≤r<∞, is properly included in Burkill’s trigonometric CP-and SCP-integrals. As an application to harmonic analysis, a de La Vallée-Poussin-type theorem for the $P_r$-integral is obtained: convergence nearly everywhere of a trigonometric series to a $P_r$-integrable function f implies that this series is the Pr-Fourier series of f.

Settore MAT/05 - Analisi MatematicaApplied MathematicsNon-absolute integral Derivative in $L^r$ Perron-type integral Cesaro-Perron integral Trigonometric series Fourier coefficients.AnalysisJournal of Mathematical Analysis and Applications
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On Variational Measures Related to Some Bases

2000

Abstract We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.

differentiation basisPure mathematicsClass (set theory)Lebesgue measureBasis (linear algebra)Henstock integralApplied MathematicsMathematical analysisvariational measureInterval (mathematics)Absolute continuityInterval functionMeasure (mathematics)δ-variationPerron integralCalculus of variationsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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