0000000000855333

AUTHOR

Antonio Boccuto

showing 2 related works from this author

A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting

2015

Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.

Pure mathematicsWeak convergenceRiesz representation theoremRiesz potential(D)-convergenceGeneral MathematicsD-convergenceMathematical analysisMathematics::Classical Analysis and ODEsHilbert spaceRiesz spaceRiesz spaceKurzweil-Henstock integralRiesz space order convergence D-convergence Kurzweil-Henstock integral Hake theoremHake theoremsymbols.namesakeRiesz–Fischer theoremM. Riesz extension theoremorder convergencesymbolsMathematics (all)Riesz–Thorin theoremMathematics
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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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