共查询到19条相似文献,搜索用时 94 毫秒
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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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近几年来,人们发现非线性偏微分方程的完全可积性和解在奇异流形处的性质密切相关.一个常微分方程解的可移奇点如果都是极点则称为具有Painleve性质.19世纪Painleve曾系统研究了二阶常微分方程的有关性质,而Kowalevskaya揭示了可积性和Painleve性质的联系.Ablowitz、Ramani和Segur猜测如果一个偏微分方程的所有相似约化得到的常微分方程都具有Painleve性质,则是完全可积方程.1983年Weiss、 相似文献
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齐次Banach空间上的算子调和分析 总被引:1,自引:0,他引:1
于树模 《数学年刊A辑(中文版)》1988,(1)
本文讨论局部紧Abel群上齐次Banach空间上的算子的调和分析,首先引进一类所谓齐次Banach空间B上的右平移可积算子,对这类算子给出了它的Fourier变换定义,它可视为通常函数Fourier变换的拓广,主要结果有:1.B上右平移可积算子的Fourier变换按强算子拓扑C-1可和于算子本身,2.B上右平移可积算子的Fourier变换将乘法和卷积两种运算相互转换,3.B上右平移可积算子具有除l、2两条外的其他形式性质,这些性质类似于普通函数Fourier变换的性质。 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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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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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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C. K. Fong 《Czechoslovak Mathematical Journal》2002,52(3):531-536
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces. 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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Czechoslovak Mathematical Journal - The space $${\cal H}{\cal K}$$ of Henstock-Kurzweil integrable functions on [a, b] is the uncountable union of Fréchet spaces $${\cal H}{\cal K}$$ (X). In... 相似文献
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A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions. 相似文献
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Erik Talvila 《Czechoslovak Mathematical Journal》2005,55(4):933-940
When a real-valued function of one variable is approximated by its nth degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue p-norms in cases where f
(n) or f
(n+1) are Henstock-Kurzweil integrable. When the only assumption is that f
(n) is Henstock-Kurzweil integrable then a modified form of the nth degree Taylor polynomial is used. When the only assumption is that f
(n) ∈ C
0 then the remainder is estimated by applying the Alexiewicz norm to Schwartz distributions of order 1.
Research partially supported by the Natural Sciences and Engineering Research Council of Canada. An adjunct appointment in
the Department of Mathematical and Statistical Sciences, University of Alberta, made valuable library and computer resources
available. 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