Approximation of functions of many variables from the generalized Nikol'skii-Besov classes in the uniform and integral metrics
DOI10.1007/S10958-024-07353-0MaRDI QIDQ6647012
Olha Ya. Radchenko, Myron I. Grom'yak, S. Ya. Yanchenko
Publication date: 3 December 2024
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
Fourier transformentire function of exponential typede la Vallée Poussin sumsgeneralized Nikol'skii-Besov classes
Harmonic analysis in one variable (42Axx) Approximations and expansions (41Axx) Harmonic analysis in several variables (42Bxx)
Cites Work
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- Approximation of functions from Nikolskii-Besov type classes of generalized mixed smoothness
- Approximation of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables by Fourier sums in the space \(L_p\) with \(p=1,\infty\)
- Approximation of the classes \(B^{\omega}_{p,\theta}\) of periodic functions of several variables by polynomials with a spectrum in cubic domains
- Approximation of functions from the isotropic Nikol'skii-Besov classes in the uniform and integral metrics
- Order estimates for the approximating characteristics of functions from the classes \(S_{p,\theta}^\Omega B(\mathbb{R}^d)\) with a given majorant of mixed modules of continuity in the uniform metric
- The infinite-dimensional widths and optimal recovery of generalized Besov classes
- Average widths and optimal recovery of multivariate Besov classes in \(L_p (\mathbb{R}^d)\)
- Approximating characteristics of the Nikol'skii-Besov classes \({S}_{1,\theta}^rB({\mathbb{R}}^d) \)
- Approximation of functions of many variables from the classes \(B_{p,\theta}^\Omega(\mathbb R^d)\) by entire functions of exponential type
- Estimations of linear widths of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables in the space \(L_q\)
- Best trigonometric and bilinear approximations of classes of functions of several variables
- Approximation of functions from isotropic \(B^{\Omega}_{1,\theta}(\mathbb R^d)\) classes by entire functions of exponential type
- Estimates for approximative characteristics of classes \(S^r_{p,\theta}B(\mathbb R^d)\) of functions in the uniform metric
- Approximative characteristics of the isotropic classes of periodic functions of many variables
- Trigonometric and orthoprojection widths of classes of periodic functions of many variables
- Approximation characteristics of the isotropic Nikol'skii-Besov functional classes
- Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form
- Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions
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