学习理论中核函数逼近的Jackson型不等式OACSTPCD
A Jackson Inequality for Kernel Function Approximation in Learning Theory
从微分算子角度理解核函数空间,借助经典Fourier变换研究核函数逼近问题.应用Fourier乘子算子和算子半群定义了一种光滑模,证明其与一种基于微分算子的K-泛函的等价性,由此给出了刻画核函数逼近收敛性的Jackson不等式.进一步证明,如果微分算子为Riesz势算子或Bessel势算子,逼近的收敛性可以转化为卷积算子逼近.特别地,给出了再生核Hilbert空间逼近的一种上界估计.
We recognize kernel function spaces from the view of differential operators and discuss the kernel function approximation problem with the classical Fourier transform.We define a modulus of smoothness with the Fourier multiplier operators associated with the semigroup of operators and show that it is equivalent to a K-functional defined with a given kernel based differential operator,with which we provide a classical Jackson-type inequality to describe the d…查看全部>>
田明党;盛宝怀
浙江越秀外国语学院经济统计系,浙江绍兴312000浙江越秀外国语学院经济统计系,浙江绍兴312000
数学
Jackson不等式K-泛函光滑模再生核Hilbert空间Riesz势算子Poisson核学习理论
Jackson-type inequalityK-functionalModulus of smoothnessReproduc-ing kernel Hilbert spaceRiesz potential operatorPoisson kernelLearning theory
《应用数学》 2023 (4)
903-914,12
Supported partially by the NSF(61877039),the NSFC/RGC Joint Research Scheme of China(12061160462 and N-CityU102/20)and the NSF of Zhejiang Province(LY19F020013)
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