Reproducing kernel Hilbert spaces and Mercer theorem

Claudio Carmeli; Ernesto De Vito; Alessandro Toigo

Reproducing kernel Hilbert spaces and Mercer theorem

泛函分析 2007-05-23 v1 数学物理 math.MP

作者: Claudio Carmeli , Ernesto De Vito , Alessandro Toigo

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.

关键词

reproducing kernel hilbert space operator theory on hilbert spaces hilbert functions

引用

@article{arxiv.math/0504071,
  title  = {Reproducing kernel Hilbert spaces and Mercer theorem},
  author = {Claudio Carmeli and Ernesto De Vito and Alessandro Toigo},
  journal= {arXiv preprint arXiv:math/0504071},
  year   = {2007}
}

备注

30 pages, Latex2e

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