TY - JOUR T1 - On M-term approximations of the Nikol’skii - Besov class AU - Akishev, G. PY - 2016 DA - April JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 297 EP - 310 VL - 45 IS - 2 LA - en AB - In this paper, we consider a Lebesgue space with a mixed norm ofperiodic functions of many variables. We obtain the exact estimationof the best M-term approximations of Nikol’skii’s and Besov’s classesin the Lebesgue space with the mixed norm. KW - Lebesgue space KW - Nikol’skii - Besov class KW - approximation CR - Akishev, G. On the exact estimations of the best M-term approximation of Besov’s class, Siberian Electronic Mathematical Reports 7, 255 – 274, 2010. CR - Akishev, G. On the order of the M-term approximation classes in Lorentz spaces, Matematical Journal. Almaty 11, (1), 5 - 29, 2011. CR - Akishev, G. On the M-term approximation Besov’s classes, International Conference “Theory of approximation of functions and its applications” dedicated to the 70-th anniversary of corresponding member of National Academy of Ukraine, professor A.I. Stepanets (1942 – 2007) May 28 - June 3, Ukraine, Kamianets-Podilsky, p. 12 , 2012. CR - Amanov, T.I. Spaces of differentiable functions with dominant mixed derivative, Alma-Ata, 1976. CR - Bazarkhanov, D.B. Estimates for certain approximation characteristics of Nikol’skii-Besov spaces with generalized mixed smoothness, Doklady Ros. Akade. Nauk 426, (1), 11 – 14, 2009. CR - Belinsky, E.S. Approximation by a ’floating’ system of exponents on the classes of smooth periodic functions, Mat. sb. 132, (1), 20 – 27, 1987. CR - Besov, O.V. Investigation of a family of functional spaces in connection with the theorems of imbedding and extension, Trudy Mat. Inst. Akad. Nauk SSSR 60, 42 - 61, 1961. CR - De Vore, R.A. Nonlinear approximation, Acta Numerica 7, 51 – 150, 1998. CR - De Vore, R.A. and Temlyakov, V.N. Nonlinear approximation by trigonometric sums, Jour. of Fourier Analysis and Applications 2, (1), 29–48, 1995. CR - Dinh Dung On asymptotic order of n-term approximations and non-linear - n widths, Vietnam Journal Math. 27, (4), 363 - 367, 1999. CR - Duan, L. The best m-term approximations on generalized Besov’s classes MBΩ q,θ with regard to orthogonal dictionaries, Journal Approximation Theory 162, 1964 – 1981, 2010. CR - Hansen, M. and Sickel, W. Best m-term approximation and Lizorkin-Triebel spaces, Journal Approximation Theory 163, 923 – 954, 2011. CR - Ismagilov, R.S. Widths of sets in linear normed spaces and the approximation of functions by trigonometric polynomials, Uspehi mathem. nauk 29, (3), 161 – 178, 1974. CR - Kashin, B.S. Approximation properties of complete orthnormal systems, Trudy Mat. Inst. Steklov 172, 187 – 201, 1985. CR - Kashin, B.S., and Sahakyan, A.A. Orthogonal series, Nauka, Moscow, 1984. CR - Lizorkin, P.I. Generalized Holder spaces B (r) p,θ and their correlation with the Sobolev spaces L (r) p , Sibirsk. Mat. Zh. 9, 1127 - 1152, 1968. CR - Maiorov, V.E. On linear widths of Sobolev classes and chains of extremal subspaces, Mat. sb. 113, (3), 437 – 463, 1980. CR - Nikol’skii, S. M. Approximation of classes of functions of several variables and embeding theorems, Nauka, Moscow, 1977. CR - Romanyuk, A.S. On the best M-term trigonometric approximations for the Besov classes of periodic functions of many variables, Izv. Ros. Akad. Nauk, Ser. Mat. 67, (2), 61 – 100, 2003. CR - Stasyuk, S.A. Best m-term trigonometric approximation for the classes Br p,θ of functions of low smoothness, Ukrain. Mathem. Journal 62, (1), 114 –122, 2010. CR - Stasyuk, S.A. Best m-term trigonometric approximation of periodic functions of several variables from Nikol’skii - Besov classes for small smoothness, Journal of Approximation Theory 177 , 1 - 16, 2014. CR - Stechkin, S.B. On the absolute convergence of orthogonal series, Doklad. Akadem. Nauk SSSR 102, (2) , 37 – 40, 1955. CR - Temlyakov, V. N. Nonlinear methods approximation, Foundations of Computational Mathematics 3, 33–107, 2003. CR - Uninskii, A.P. Inequalities for entire functions and trigonometric polynomials with mixed norm, Proceeding of the All-Union Symposium on embedding theorems, ( Baku - 1966) - M.: Nauka, 112 - 118, 1970. UR - https://dergipark.org.tr/en/pub/hujms/issue//524184 L1 - https://dergipark.org.tr/en/download/article-file/644498 ER -