\(n\)-best kernel approximation in reproducing kernel Hilbert spaces (Q6051151)

The paper considers a class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc. The existence of \(n\)-best kernel approximation under the norm of such a reproducing kernel Hilbert space is investigated. Assuming that the reproducing kernel satisfies an analyticity condition, an infinite-norm property, and a uniform boundedness condition, the existence is proved. Applications to the classical Hardy space, weighted Hardy spaces, and stochastic \(n\)-best approximation are also discussed.