Search results for " integral transform."

showing 4 items of 4 documents

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 Software Tool for the Exponential Power Distribution: The normalp Package

2005

In this paper we present the normalp package, a package for the statistical environment R that has a set of tools for dealing with the exponential power distribution. In this package there are functions to compute the density function, the distribution function and the quantiles from an exponential power distribution and to generate pseudo-random numbers from the same distribution. Moreover, methods concerning the estimation of the distribution parameters are described and implemented. It is also possible to estimate linear regression models when we assume the random errors distributed according to an exponential power distribution. A set of functions is designed to perform simulation studi…

Statistics and ProbabilityExponential distributionTheoretical computer scienceComputer scienceAsymptotic distributionDistribution fittingLaplace distributionExponential familyGamma distributionStatistics Probability and UncertaintyNatural exponential familyProbability integral transformAlgorithmlcsh:Statisticslcsh:HA1-4737exponential power distribution R estimation linear regressionSoftwareJournal of Statistical Software
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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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Inversion formulae for the integral transform on a locally compact zero-dimensional group

2009

Abstract Generalized inversion formulae for multiplicative integral transform with a kernel defined by characters of a locally compact zero-dimensional abelian group are obtained using a Kurzweil-Henstock type integral.

Locally compact zero-dimensional abelian group characters of a group Kurzweil-Henstock integral Fourier series multiplicative integral transform inversion formulaSettore MAT/05 - Analisi MatematicaGeneral MathematicsMultiplicative functionMathematical analysisMathematics::Classical Analysis and ODEsLocally compact spaceAbelian groupLocally compact groupIntegral transformInversion (discrete mathematics)MathematicsTatra Mountains Mathematical Publications
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