• Korean Journal of Mathematics
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• v.28 no.4
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• pp.973-984
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• 2020

This paper is devoted to study the reproducing property on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi variable computing, this structures play the key role in probability, mathematical finance and machine learning.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.523-537
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• 2021

In this paper, we obtain some new inequalities for the Berezin number of operators on reproducing kernel Hilbert spaces by using the Hölder-McCarthy operator inequality. Also, we give refine generalized inequalities involving powers of the Berezin number for sums and products of operators on the reproducing kernel Hilbert spaces.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• The Korean Journal of Applied Statistics
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• v.33 no.5
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• pp.569-578
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• 2020

By estimating conditional quantile functions of the response, quantile regression (QR) can provide comprehensive information of the relationship between the response and the predictors. In addition, kernel quantile regression (KQR) estimates a nonlinear conditional quantile function in reproducing kernel Hilbert spaces generated by a positive definite kernel function. However, it is infeasible to use the KQR in analysing a massive data due to the limitations of computer primary memory. We propose a divide and conquer based KQR (DC-KQR) method to overcome such a limitation. The proposed DC-KQR divides the entire data into a few subsets, then applies the KQR onto each subsets and derives a final estimator by aggregating all results from subsets. Simulation studies are presented to demonstrate the satisfactory performance of the proposed method.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.23-37
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• 2011

In this paper, we use a modified Tikhonov regularization method to solve the Fredholm integral equation of the first kind. Under the assumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of measured points. Some numerical experiments show that the proposed method is effective and stable.