Exact order of approximation of periodic functions by one nonclassical method of summation of Fourier series
- 61 Downloads
By using an exact estimate for approximation by known trigonometric polynomials, we strengthen a Jackson-type theorem. Moreover, we determine the exact order of approximation of some periodic functions by these polynomials. For this purpose, we introduce a special modulus of smoothness.
Unable to display preview. Download preview PDF.
- 1.A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).Google Scholar
- 6.E. M. Stein and G. Weiss, Introduction to Fourier Analysis of Euclidean Spaces, Princeton University, Princeton (1971).Google Scholar
- 8.E. Liflyand, S. Samko, and R. Trigub, “TheWiener algebra of absolutely convergent Fourier integrals: an overview,” Anal. Math. Phys., 2, 1–68 (2012); E. Liflyand, S. Samko, and R. Trigub, Known and New Results on Absolute Convergence of Fourier Integrals, Preprint No. 859, Centre de Recerca Matemàtica (2009).Google Scholar