Griebel, MichaelMichaelGriebelRieger, ChristianChristianRiegerZwicknagl, BarbaraBarbaraZwicknagl2022-03-052022-03-052018https://publica.fraunhofer.de/handle/publica/25538810.1007/s10208-017-9346-zWe present a theoretical framework for reproducing kernel-based reconstruction methods in certain generalized Besov spaces based on positive, essentially self-adjoint operators. An explicit representation of the reproducing kernel is given in terms of an infinite series. We provide stability estimates for the kernel, including inverse Bernstein-type estimates for kernel-based trial spaces, and we give condition estimates for the interpolation matrix. Then, a deterministic error analysis for regularized reconstruction schemes is presented by means of sampling inequalities. In particular, we provide error bounds for a regularized reconstruction scheme based on a numerically feasible approximation of the kernel. This allows us to derive explicit coupling relations between the series truncation, the regularization parameters and the data set.en003510005006518journal article