Geodesic
The problem of continuation with least coanalytic deviation
Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 45-57

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The problem of continuing a function from the unit circle to the unit disk so that the continuation has the least deviation from the Sobolev subspace of analytic functions is considered. A mathematical model of this problem is constructed. It is proved that the problem is well-posed. 
@article{MZM_1998_64_1_a5,
     author = {Yu. A. Dubinskii},
     title = {The problem of continuation with least coanalytic deviation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {45--57},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a5/}
}
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Yu. A. Dubinskii. The problem of continuation with least coanalytic deviation. Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 45-57. http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a5/