Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions
نویسندگان
چکیده
منابع مشابه
Banach-valued Henstock-kurzweil Integrable Functions Are Mcshane Integrable on a Portion
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
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Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...
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We will study the Henstock–Kurzweil delta and nabla integrals, which generalize the Henstock–Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Hensock–Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases.
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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...
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Some recent results related to the P-adic derivatives and integrals are surveyed. Applications of the Henstock-Kurzweil P-integral and the Perron P-integral to the problem of recovering the coefficients of series with respect to the Vilenkin system and the Haar system (both in one dimension and in higher dimensions) are discussed. The case of the continual analogue of the Vilenkin system is als...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2011
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-011-0050-x