Approximation of Sobolev classes by polynomials and ridge functions |
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| Authors: | VN Konovalov D Leviatan VE Maiorov |
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| Institution: | aInstitute of Mathematics, NAS of Ukraine, 01601 Kyiv, Ukraine;bRaymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel;cTechnion I.I.T., 32000 Haifa, Israel |
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| Abstract: | Let  be the usual Sobolev class of functions on the unit ball  in  , and  be the subclass of all radial functions in  . We show that for the classes  and  , the orders of best approximation by polynomials in  coincide. We also obtain exact orders of best approximation in  of the classes  by ridge functions and, as an immediate consequence, we obtain the same orders in  for the usual Sobolev classes  . |
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| Keywords: | Sobolev classes Radial functions Polynomials Ridge functions |
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