VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM

被引：133

作者：

Carmeli, Claudio ^{[1
,2
]}

De Vito, Ernesto ^{[2
,3
]}

Toigo, Alessandro ^{[1
,2
]}

机构：

[1] Univ Genoa, Dipartimento Fis, I-16146 Genoa, Italy

[2] Ist Nazl Fis Nucl, Sez Genova, I-16146 Genoa, Italy

[3] Univ Modena & Reggio Emilia, Dipartmento Matemat, I-41100 Modena, Italy

来源：

ANALYSIS AND APPLICATIONS | 2006年 / 4卷 / 04期

关键词：

Reproducing kernel Hilbert space; Mercer theorem; integral operator;

D O I：

10.1142/S0219530506000838

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.

引用

页码：377 / 408

页数：32

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