Variational Theory of Splines

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This title is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form, including existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, and dimensional reducing (traces of splines onto manifolds). All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.