Abstract
In this paper, we study the informativeness of linear functionals in reconstruction problems and obtain exact orders of the informativeness of linear functionals in the Besov and Sobolev classes W and SW.
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REFERENCES
N. Temirgaliev, “Number-theoretic methods and the probability-theoretic approach to problems in calculus. The theory of embeddings and approximations, absolute convergence, and the transformation of Fourier series,” Vestnik Evraz. Univ. (1997), no. 3, 90–144.
N. M. Korobov, Number-Theoretic Method in Approximate Analysis [in Russian], Fizmatgiz, Moscow, 1963.
N. M. Korobov, Trigonometric Sums and Their Applications [in Russian], Nauka, Moscow, 1989.
S. A. Smolyak, “Quadrature and interpolation formulas on tensor products of some classes of functions,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 148 (1963), no. 5, 1042–1045.
K. K. Frolov, “Upper bounds for the errors of quadrature formulas on classes of functions,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 231 (1976), no. 4, 818–821.
Loo Keng Hua and Yang Wang, Application of Number Theory to Numerical Analysis, Springer-Verlag, Berlin–Heidelberg–New York, 1981.
V. N. Temlyakov, “Approximate reconstruction of functions of several variables,” Mat. Sb. [Math USSR-Sb.], 228 (1985), no. 2, 256–268.
M. M. Skriganov, “On lattices in fields of algebraic numbers,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 306 (1980), no. 3, 353–355.
S. M. Voronin, “On interpolation formulas for a class of Fourier polynomials,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 61 (1997), no. 4, 19–35.
S. N. Kudryavtsev, “The best accuracy in the reconstruction of functions of finite smoothness from their values at a given number of points,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 62 (1998), no. 1, 21–58.
N. Temirgaliev, “Application of divisor theory to the approximate reconstruction and integration of periodic functions of several variables,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 310 (1990), no. 5, 1050–1054.
K. Sherniyazov, Approximate Reconstruction of Functions and of Solutions of the Heat Equation with Distribution Functions of Initial Temperatures from the Classes E SW,and B, Kandidat thesis in the physico-mathematical sciences [in Russian], Al-Farabi Kazakh State Univ., Alma-Ata, 1998.
S. M. Nikol'skii, Approximation of Function of Several Variable and Embedding Theorems [in Russian], Nauka, Moscow, 1977.
S. V. Kurosh, A Course in Higher Algebra [in Russian], Nauka, Moscow, 1978.
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Azhgaliev, S., Temirgaliev, N. Informativeness of Linear Functionals. Mathematical Notes 73, 759–768 (2003). https://doi.org/10.1023/A:1024037410770
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DOI: https://doi.org/10.1023/A:1024037410770