Geodesic
Nonlinear interpolation and norm minimization
Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 512-524

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We prove that the set of convolution-type functions in $\mathbb R_d$ that satisfy the interpolation conditions contains a unique function whose convolution element has the minimum $L_p$-norm. The extremal function is determined by solving a nonlinear interpolation problem. The results are applied to an operator recovery problem. 
@article{MZM_1995_58_4_a3,
     author = {A. A. Zhensykbaev},
     title = {Nonlinear interpolation and norm minimization},
     journal = {Matemati\v{c}eskie zametki},
     pages = {512--524},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a3/}
}
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A. A. Zhensykbaev. Nonlinear interpolation and norm minimization. Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 512-524. http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a3/