Geodesic
Estimates of rate of convergence of best approximations by local functions
Zapiski Nauchnykh Seminarov POMI, Computational methods and automatic programming, Tome 58 (1976), pp. 22-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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Questions are considered on the rate of convergence (in some abstract space of functions) of approximations that are the best in another space. Under specific conditions it is shown that the best approximations by local functions in a weighted Sobolev space $W^r_{p,B}$ yield almost-best approximation $W^r_{q,B}$ with $q\in[p,+\infty)$. 
@article{ZNSL_1976_58_a2,
     author = {Yu. K. Dem'yanovich},
     title = {Estimates of rate of convergence of best approximations by local functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {22--37},
     year = {1976},
     volume = {58},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_58_a2/}
}
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Yu. K. Dem'yanovich. Estimates of rate of convergence of best approximations by local functions. Zapiski Nauchnykh Seminarov POMI, Computational methods and automatic programming, Tome 58 (1976), pp. 22-37. http://geodesic.mathdoc.fr/item/ZNSL_1976_58_a2/