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On the differentiability of vector valued additive set functions
(Scientific Research, http://www.scirp.org, 2013-11)
The Lebesgue-Nikodým Theorem states that for a Lebesgue measure λ:Σ〖⊂2〗^Ω→[0,∞) an additive set function F:Σ→R which is λ-absolutely continuous is the integral of a Lebegsue integrable a measurable function ...
Unified approach to vector valued integration
(Pushpa Publishing House, www.pphmj.com, 2013-06)
We introduce a natural and more flexible approach to the definition of vector valued integral that will completely forgo any measurability assumption, strengthen the existing various classical concepts of ...
Exponential polynomials on commutative hypergroups
(Springer, www.springer.com, 2013)
Polynomials and exponential polynomials play a fundamental role in the theory of spectral analysis and spectral synthesis on commutative groups. Recently several new results have been published in this field. Spectral ...
More on equivalence properties of Radon-Nikodym property types and Complete Continuity property types
(Pushpa Publishing House, www.pphmj.com, 2013-01)
We study the equivalence property of the I- and II-L-Radon-Nikodým property (resp. I- and II-L-complete continuity property) types of Banach spaces. As a by-product, we obtain a proof of the following: F. Lust-Picard’s ...
The Levi-Civitá equation, vector modules and spectral synthesis
(Banach Center Polish Academy of Sciences, 2013)
The purpose of this paper is to give a survey on some recent results concerning spectral analysis and spectral synthesis in the framework of vector modules and in close connection with the Levi-Civita functional equation. ...