Bounded linear functionals on the space of Henstock-Kurzweil integrable functions
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منابع مشابه
ON THE DUAL SPACE OF THE HENSTOCK-KURZWEIL INTEGRABLE FUNCTIONS IN N DIMENSIONS* Tepper
The dual space of the class of Henstock-Kurzweil integrable functions is well known in the one-dimensional case and corresponds to the space of multipliers which, in turn, coincides with the class of functions of bounded essential variation. Comparable results in higher dimensions have been elusive. For cases in which the partitions defining the Henstock-Kurzweil integrals are defined on n-cell...
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and Applied Analysis 3 Then, as L[a, b] ⊂ HK([a, b]) it holds that dim(L[a, b]) ≤ dim(HK([a, b])) ≤ card(HK([a, b])). Therefore, by Lemma 8, Corollary 7 and the known fact that c0 = c, we obtain the desired conclusion. Hereafter, the Alexiewicz topology and the topology induced by the norm of Proposition 9 will be denoted as τ A and τ ‖⋅‖ , respectively. Proposition 10. The topology τ ‖⋅‖ on HK...
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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m-dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f : [0, 1] −→ and a continuous function F : [0, 1] −→ such that
متن کاملHenstock–Kurzweil Fourier transforms
The Fourier transform is considered as a Henstock–Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann–Lebesgue lemma fails: Henstock– Kurzweil Fourier transforms can have arbitrarily large point-wise growth. Convolution and inversion theorems are established. An appen...
متن کاملHenstock-Kurzweil Integral Transforms
Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2009
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-009-0070-y