English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we study $L_2$-norm sampling discretization and samplingrecovery of complex-valued functions in RKHS on $D \subset \R^d$ based onrandom function samples. We only assume the finite trace of the kernel(Hilbert-Schmidt embedding into $L_2$) and provide several concrete estimateswith precise constants for the corresponding worst-case errors. In general, ouranalysis does not need any additional assumptions and also includes the case ofnon-Mercer kernels and also non-separable RKHS. The fail probability iscontrolled and decays polynomially in $n$, the number of samples. Under themild additional assumption of separability we observe improved rates ofconvergence related to the decay of the singular values. Our main tool is aspectral norm concentration inequality for infinite complex random matriceswith independent rows complementing earlier results by Rudelson, Mendelson,Pajor, Oliveira and Rauhut.

$L_2$-norm sampling discretization and recovery of functions from RKHS with finite trace