Search results for "Locally compact group"

showing 6 items of 6 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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A Note on Locally ??-compact Spaces

1995

: The local version of the concept of ℰτ-compactness (where ℰ is a class of Hausdorff spaces and ℰ is a cardinal) introduced by the first author as a generalization of Her-rlich's concept of ℰ-compactness (and hence, also of Mrowka's E-compactness) is defined and the corresponding theory is initiated. An essential part of the theory is developed under the additional assumption that all spaces from ℰ are absolute extensors for spaces under consideration. The theory contains as a special case the classical theory of local compactness.

Class (set theory)Pure mathematicsRiesz–Markov–Kakutani representation theoremGeneral NeuroscienceVague topologyHausdorff spaceMathematics::General TopologyLocally compact groupContinuous functions on a compact Hausdorff spaceGeneral Biochemistry Genetics and Molecular BiologyCompact spaceHistory and Philosophy of ScienceRelatively compact subspaceMathematicsAnnals of the New York Academy of Sciences
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Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group

2009

Abstract A Kurzweil-Henstock type integral defined on a zero-dimensional compact abelian group is studied and used to obtain a generalization of some results related to the problem of recovering, by generalized Fourier formulae, the coefficients of convergent series with respect to the characters of such a group.

General MathematicsMathematical analysisMathematics::Classical Analysis and ODEsLocally compact groupFourier integral operatorsymbols.namesakeFourier transformSettore MAT/05 - Analisi MatematicaFourier analysisImproper integralsymbolsAbelian groupCompact zero-dimensional group characters of group Kurzweil-Hestock integral Perrron integral Fourier series coefficient problem.Fourier seriesConvergent seriesMathematicsTatra Mountains Mathematical Publications
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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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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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Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

2009

Abstract Denjoy and P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform.

Settore MAT/05 - Analisi MatematicaGeneral MathematicsPath integral formulationMultiplicative functionMathematical analysisLocally compact spaceDenjoy integral multiplicative transformsAbelian groupLocally compact groupIntegral transformInversion (discrete mathematics)MathematicsVolume integral
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