Approximation of differentiable functions of two variables in the mean by fourier sums
Copyright policy )Approximation of differentiable functions of two variables in the mean by fourier sums
This equation gives the solution of the Kolmogorov--Nikol'skii problem if c1~m/n~ci, where ci and c2 are positive constants, since the first term on the right-hand side is the principal term in this case only. We prove the following theorem. TI{EOREH i. For p =i and p =~ the following equation is valid for arbitrary natural numbers m and n: 16 ln m ln n 4 Into 4 Inn ( In mn 1 1 ) g.~,~(A;) zO (m z+n2) ~ @ ~z m2~ q-z~ z n2 ' + 0 ( m ~ @ n i ) ~ _ [ _ _ ~ _ 1 ~ . . ( 2 )
- Russian Academy of Sciences Russian Federation
Fourier series and coefficients in several variables, Kolmogorov- Nikol'skii problem, asymptotic behaviour, rectangular Fourier sums, Sobolev generalized derivatives, norm of best approximation, Cesaro means
Fourier series and coefficients in several variables, Kolmogorov- Nikol'skii problem, asymptotic behaviour, rectangular Fourier sums, Sobolev generalized derivatives, norm of best approximation, Cesaro means
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