Regularized Kernel-Based Reconstruction in Generalized Besov Spaces

We 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.