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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     author = {A. I. Rozhenko},
     title = {Spline approximation in tensor product spaces},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {373--390},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a7/}
}
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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/