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Summary Five interesting theorems of Konyushkov giving estimations for the best approximation in terms of the coefficients of a Fourier series are generalized or extended to the cases when the monotone or quasi-monotone coefficients are replaced by sequences of rest bounded variation of coefficients.
Summary
Recently we extended some interesting theorems of Konyushkov giving estimations for the best approximation by the coefficients of the Fourier series of the function in question. We replaced the monotone or quasi-monotone coefficient sequences by coefficient sequences of rest bounded variation. In this note both notions are generalized for such coefficient sequences where certain restriction is given only in terms of the "rest variation" of the sequence.
Резуме
Получены точные по порядку оценки ортопроекционных и линейных поперечников классов B p,θ r периодических функций многих переменных в пространстве L q , 1 ≤ p, q, ≤ ∞. Установлен порядок наилучшего приближения в пространстве L ∞ классов B ∞,θ r периодических функций двух переменных тригонометрическими полиномами с «номерами» гармоник иэ гиперболического креста.
approximation and moduli of smoothness . Doctorat en Matematiques Universitat Autonoma de Barselona Departament de Matematiques, Febrer 2018 , 1 – 119 . [13] A . Jumabayeva . Liouville-Weyl derivatives, best approximation, and moduli of smoothness . Acta
-9939-1988-0938668-8 . [8] Ditzian , Z. 1998 Fractional derivatives and best approximation Acta Math. Hungar. 81 323 – 348 10.1023/A:1006554907440
