Geodesic
Spline approximation in tensor product spaces
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 373-390.

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The normal solvability of the energy operator for spline approximation problem in tensor product of abstract Hilbert spaces is proved. Hence, the correctness of the problem (the existence of a solution) is derived. The general method for the regularization of a semi-Hilbert space reproducing map is proposed. It allows to construct the reproducing map in tensor case. The general theory is illustrated by examples. 
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A. I. Rozhenko. Spline approximation in tensor product spaces. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 373-390. http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a7/

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