Approximation of classes of functions of many variables by their orthogonal projections onto subspaces of trigonometric polynomials
- 16 Downloads
In the spaceL q, 1<q<∞ we establish estimates for the orders of the best approximations of the classes of functions of many variablesB 1,θ r andB p,α r by orthogonal projections of functions from these classes onto the subspaces of trigonometric polynomials. It is shown that, in many cases, the estimates obtained in the present work are better in order than in the case of approximation by polynomials with harmonics from the hyperbolic cross.
KeywordsPeriodic Function Orthogonal Projection Trigonometric Polynomial Ukrainian Academy Mixed Derivative
Unable to display preview. Download preview PDF.
- 1.S. M. Nikol’skii,Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow 1969.Google Scholar
- 4.E. S. Belinskii “Approximation by floating systems of exponents in classes of periodic functions with bounded mixed derivative,” in:Investigations in the Theory of Functions of Many Real Variables [in Russian], Yaroslavl’ (1988), pp. 16–33.Google Scholar
- 5.A. S. Romanyuk, “Approximation of the classesB p,θr of periodic functions of many variables by partial Fourier sums with arbitrary choice of harmonics,” in:Fourier Series: Theory and Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 112–118.Google Scholar
- 6.A. S. Romanyuk, “On the approximation of the Besov classes of functions of many variables by partial sums with given number of harmonics,” in:Optimization of Approximation Methods [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 70–78.Google Scholar
- 7.V. N. Temlyakov, “Approximations of functions with bounded mixed derivative,”Tr. Mat. Inst. Akad. Nauk SSSR, 178 (1986).Google Scholar
- 9.N. P. Korneichuk,Exact Constants in the Theory of Approximations [in Russian], Nauka, Moscow (1987)Google Scholar