ESTIMATES OF M–TERM APPROXIMATIONS OF FUNCTIONS OF SEVERAL VARIABLES IN THE LORENTZ SPACE BY A CONSTRUCTIVE METHOD
Akishev G.
2024L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2024#15Issue 28 - 32 pp.
In the paper, the Lorentz space Lq,τ (Tm) of periodic functions of several variables, the Nikol’skii–Besov class S ¯r q,τ,θB and the associated class Wa,b,¯r q,τ for 1 < q, τ < ∞, 1 ≤ θ ≤ ∞ are considered. Estimates are established for the best M-term trigonometric approximations of functions of the classes Wa,b,¯r q,τ1 and S ¯r q,τ,θB in the norm of the space Lp,τ2 (Tm) for different relations between the parameters q, τ1, p, τ2, a, θ. The proofs of the theorems are based on the constructive method developed by V.N. Temlyakov.
best M–term approximation , constructive method , Lorentz space , Nikol’skii–Besov class
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Department of Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 11 Kazhymukan St,Kazakhstan Branch, Astana, 010010, Kazakhstan
Institute of mathematics and mathematical modeling, 125 Pushkin St, Almaty, 050010, Kazakhstan
Institute of Natural Sciences and Mathematics, Ural Federal University, 4 Turgenov St., Yekaterinburg, 620002, Russian Federation
Department of Fundamental and Applied Mathematics
Institute of mathematics and mathematical modeling
Institute of Natural Sciences and Mathematics
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