共查询到20条相似文献,搜索用时 125 毫秒
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该文建立了Henstock-Kurzweil 可积函数的 Laplace变换, 讨论了其基本性质及解析性质, 得到Henstock-Kurzweil可积意义下的反演公式, 并给出反例说明这一结果不能改进 相似文献
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广义函数Denjoy积分的收敛性问题 总被引:2,自引:0,他引:2
本文讨论广义函数De njoy积分的收敛性问题.首先给出了广义Denjoy可积函数空间中强收敛、弱收敛、弱~*收敛和广义函数Denjoy积分收敛的关系;证明拟一致收敛是广义函数Denjoy积分收敛的一个充分必要条件;最后指出了Denjoy可积广义函数列弱~*收敛与强收敛等价当且仅当原函数等度连续. 相似文献
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在研究Bochner可积函数空间上线性算子的积分表示时,一般总要求函数值域空间X具有Radon-Nikodym性质.本文从线性算子本身出发,在不要求X具有Radon-Nikodym性质的条件下研究线性算子的积分表示,给出一个充要条件. 相似文献
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本文研究了近似连续C-可积函数的原函数问题.利用近似连续C-积分的有关性质,得到了函数近似C-可积的一个充分必要条件,推广了B.Bongiorno等人的工作. 相似文献
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本文研究了高维空间中C-积分的有关性质.利用被积函数的可测性质,证明了若函数在I0上C-可积,则存在I0上的一个部分,使得函数在该部分上Lebesgue可积.推广了文献[6]中的结论. 相似文献
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R.AGordon在[1]中定义了从R1到Banach空间抽象函数的McShane积分,证明了当X不含C0时,如果f在[a,b]上McShanef可积,则在[a,b]上Petits 可积.在这篇文章中,我们定义了从Rn到Banaach空间抽象函数的Mcshane积分,证明了fMcShane可积,则f是Pattis可积.于是我们推广了[1]的结果. 相似文献
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S. Heikkilä 《Journal of Mathematical Analysis and Applications》2011,377(1):286-295
In this paper we prove monotone convergence theorems for Henstock-Kurzweil integrable functions from a compact real interval to an ordered Banach space. These theorems are then applied to prove existence results for solutions of a discontinuous functional integral equation containing Henstock-Kurzweil integrable functions. 相似文献
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In this paper,we construct directly absolutely continuous major and minor functions of a function which is Lebesque integrable ,and we also construct directly continuous major and minor functions of a function which is Henstock-Kurzweil integrable. 相似文献
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The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties
of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration).
It is shown that the indefinite McShane product integral of a matrix-valued function A is absolutely continuous. As a consequence we obtain that the McShane product integral of A over [a, b] exists and is invertible if and only if A is Bochner integrable on [a, b].
Supported by grant No. 201/04/0690 of the Grant Agency of the Czech Republic. 相似文献
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S. Heikkilä 《Journal of Mathematical Analysis and Applications》2011,379(1):171-179
In this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing Henstock-Kurzweil integrable functions. 相似文献
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Allan Peterson Bevan Thompson 《Journal of Mathematical Analysis and Applications》2006,323(1):162-178
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 Henstock-Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases. 相似文献
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Tuo-Yeong Lee 《Czechoslovak Mathematical Journal》2008,58(4):1221-1231
In this paper we show that the measure generated by the indefinite Henstock-Kurzweil integral is F
σδ
regular. As a result, we give a shorter proof of the measure-theoretic characterization of the Henstock-Kurzweil integral. 相似文献
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Tuo-Yeong Lee 《Czechoslovak Mathematical Journal》2009,59(4):1005-1017
Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation
theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence
and equality of two iterated Henstock-Kurzweil integrals. 相似文献
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Lee Tuo-Yeong 《Czechoslovak Mathematical Journal》2005,55(3):625-637
Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil
integrals in the Euclidean space. 相似文献
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Tuo-Yeong Lee 《Journal of Mathematical Analysis and Applications》2006,323(1):741-745
This paper is a continuation of the paper [T.Y. Lee, Product variational measures and Fubini-Tonelli type theorems for the Henstock-Kurzweil integral, J. Math. Anal. Appl. 298 (2004) 677-692], in which we proved several Fubini-Tonelli type theorems for the Henstock-Kurzweil integral. Let f be Henstock-Kurzweil integrable on a compact interval . For a given compact interval , set
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In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one. 相似文献