INCREASING LIMIT OF REPRODUCING KERNELS

被引：0

作者：

Yoo, Hyun Jae ^{[1
]}

机构：

[1] Hankyong Natl Univ, Dept Appl Math, Anseong 456749, Gyeonggi Do, South Korea

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2011年 / 41卷 / 05期

关键词：

Reproducing kernel Hilbert space; restriction and extension of reproducing kernels; increasing sequence of reproducing kernels;

D O I：

10.1216/RMJ-2011-41-5-1741

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the limit of increasing reproducing kernels and construct the corresponding reproducing kernel Hilbert space. Given an increasing sequence of reproducing kernel Hilbert spaces with their norms decreasing, we can find a limit of the sequence of those reproducing kernels. Thereby we can construct a reproducing kernel Hilbert space on a subset of common underlying sets. The proof corrects an error in that of Aronszajn. We discuss the error by giving an example.

引用

页码：1741 / 1754

页数：14

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