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The present paper establishes a fact which, in the terminology adopted in the theory of approximation, is called the inverse theorem. The case in point is that if a function, continuous in a set, can be approximated at a given rate at some appropriate scale by some pool of approximating functions, then it has a well-defined smoothness. If, in addition, it is known that functions of smoothness considered can be approximated at a required rate, we obtain a constructive description of the smoothness class in terms of the rate of approximation.
Original language | English |
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Pages (from-to) | 318-323 |
Number of pages | 6 |
Journal | Vestnik St. Petersburg University: Mathematics |
Volume | 41 |
Issue number | 4 |
DOIs | |
State | Published - 1 Dec 2008 |
ID: 48397931