References
-
Akishev G.A.
The ortho-diameters of Nikol'skii and Besov classes in the Lorentz spaces.
Russian Math. (Iz. VUZ) 2009, 53 (2), 21-29.
doi: 10.3103/S1066369X09020029
(translation of Izv. Vyssh. Uchebn. Zaved. Mat. 2009, 2, 25-33. (in Russian))
-
Amanov T.I.
Representation and embedding theorems for function spaces $S^{(r)}_{p,\theta}B(\mathbb{R}_n)$ and $S^{(r)}_{p,\theta^*}B,$ \ $(0\leq x_j\leq2\pi; j=1,\ldots,n)$.
Tr. Mat. Inst. Steklova 1965, 77, 5-34. (in Russian)
-
Andrianov A.V., Temlyakov V.N.
On Two Methods of Generalization of Properties of Univariate Function Systems to Their Tensor Product.
Proc. Steklov Inst. Math. 1997, 219, 25-35.
(translation of Tr. Mat. Inst. Steklova 1997, 219, 32-43. (in Russian))
-
Balgimbayeva S.A., Smirnov T.I.
Estimates of The Fourier Widths of the Classes Of Periodic Functions With Given Majorant of the Mixed Modulus of Smoothness.
Sib. Math. J. 2018, 59 (2), 217-230.
doi: 10.1134/S0037446618020040
(translation of Sibirsk. Mat. Zh. 2018, 59 (2), 277-292.
doi: 10.17377/smzh.2018.59.204
(in Russian))
-
Bari N.K., Stechkin S.B.
The best approximations and differential properties of two conjugate functions.
Trans. Moscow Math. Soc. 1956, 5, 483-522. (in Russian)
-
Bazarkhanov D.B.
Estimates of the Fourier widths of classes of Nikol'skii-Besov and Lizorkin-Triebel
types of periodic functions of several variables.
Math. Notes 2010, 87 (1-2), 281-284.
doi: 10.1134/S0001434610010359
(translation of Mat. Zametki 2010, 87 (2), 305-308.
doi: 10.4213/mzm8592
(in Russian))
-
Belinsky E.S.
Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative.
J. Approx. Theory 1998, 93, 114-127.
doi: 10.1006/jath.1997.3157
-
Bernstein S.N.
Collected work. Vol. II. Constructive theory of functions (1931-1953). Nauka, Moscow, 1954. (in Russian)
-
D$\rm\tilde{u}$ng D.
Approximation by trigonometric polynomials of functions of several variables on the torus.
Sb. Math. 1988, 59 (1), 247-267.
doi: 10.1070/SM1988v059n01ABEH003134
(translation of Mat. Sb. 1986, 131(173) (2), 251-271. (in Russian))
-
D$\rm\tilde{u}$ng D., Temlyakov V.N., Ullrich T.
Hyperbolic Cross Approximation.
Birkhauser, Basel, 2018.
-
Fedunyk O.V.
Estimates of approximation characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables in the space $L_{q}$.
Approx. Theory of Functions and Related Problems: Proc. Inst. Math. NAS
Ukr. 2005, 2 (2), 268-294. (in Ukrainian)
-
Fedunyk-Yaremchuk O.V., Hembars'ka S.B.
Estimates of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given
majorant of mixed moduli of continuity in the space $L_{q}$.
Carpathian Math. Publ. 2019, 11 (2), 281-295.
doi: 10.15330/cmp.11.2.281-295
-
Galeev E.M.
Orders of the orthoprojection widths of classes of periodic functions of one and of several variables.
Math. Notes 1988, 43 (2), 110-118.
doi: 10.1007/BF01152547
(translation of Mat. Zametki 1988, 43 (2), 197-211. (in Russian))
-
Hembars'kyi M.V., Hembars'ka S.B.
Approximate characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of one variable and many ones.
J. Math. Sci. (N.Y.) 2019, 242 (6), 820-832.
doi: 10.1007/s10958-019-04518-0
(translation of Ukr. Mat. Visn. 2019, 16 (1), 88-104. (in Ukrainian))
-
Hembarskyi M.V., Hembarska S.B., Solich K.V.
The best approximations and widths of the classes of periodic functions of one and several variables in the space $B_{\infty,1}$.
Mat. Stud. 2019, 51 (1), 74-85.
doi: 10.15330/ms.51.1.74-85
(in Ukrainian)
-
Lizorkin P.I., Nikol'skii S.M.
Spaces of functions with mixed smoothness from the decomposition point of view.
Proc. Steklov Inst. Math. 1990, 187, 163-184.
(translation of Tr. Mat. Inst. Steklova 1989, 187, 143-161. (in Russian))
-
Marcinkiewicz J.
Quelques remarques Quelques remarques sur l'interpolation.
Acta Sci. Math. (Szeged), 1937, 8 (2-3), 127-130. (in French)
-
Nikol'skii S.M.
Functions with dominant mixed derivative, satisfying a multiple Holder condition.
Sibirsk. Mat. Zh. 1963, 4 (6) 1342-1364. (in Russian)
-
Pustovoitov N.N.
Representation and approximation of periodic functions of several variables with given mixed modulus of continuity.
Anal. Math. 1994, 20, 35-48.
doi: 10.1007/BF01908917
(in Russian)
-
Pustovoitov N.N.
The orthowidths of classes of multidimensional periodic functions, for which the majorant of mixed continuity moduli contains power and
logarithmic multipliers.
Anal. Math. 2008, 34, 187-224.
doi: 10.1007/s10476-008-0303-6
(in Russian)
-
Romanyuk A.S.
Approximability of the classes $ B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations.
Sb. Math. 2004, 195 (2), 237-261.
doi: 10.1070/SM2004v195n02ABEH000801
(translation of Mat. Sb. 2004, 195 (2), 91-116.
doi: 10.4213/sm801
(in Russian))
-
Romanyuk A.S.
Approximation characteristics and properties of operators of the best approximation of classes of functions from Sobolev and Nikol'skii-Besov spaces.
Ukr. Mat. Visn. 2020, 17 (3), 372-395. (in Ukrainian)
-
Romanyuk A.S.
Approximative Characteristics of the Classes of Periodic Functions of Many Variables.
Proc. of the Institute of Mathematics of the NAS of Ukraine, Kiev, 2012, 93. (in Russian)
-
Romanyuk A.S.
Diameters and best approximation of the classes $B^r_{p,\theta}$ of periodic functions of several variables.
Anal. Math. 2011, 37, 181-213.
doi: 10.1007/s10476-011-0303-9
(in Russian)
-
Romanyuk A.S.
Estimates for Approximation Characteristics of the Besov Classes $B^{r}_{p,\theta}$ of Periodic Functions of Many Variables in the Space $L_q$. I.
Ukrain. Math. J. 2001, 53 (9), 1473-1482.
doi: 10.1023/A:1014314708184
(translation of Ukrain. Mat. Zh. 2001, 53 (9), 1224-1231. (in Russian))
-
Romanyuk A.S.
Estimates for Approximation Characteristics of the Besov Classes $B^{r}_{p,\theta}$ of Periodic Functions of Many Variables in the Space $L_q$. II.
Ukrain. Math. J. 2001, 53 (10), 1703-1711.
doi: 10.1023/A:1015200128349
(translation of Ukrain. Mat. Zh. 2001, 53 (10), 1402-1408. (in Russian))
-
Romanyuk A.S., Romanyuk V.S.
Approximating characteristics of the classes of periodic multivariate functions in the space $B_{\infty,1}$.
Ukrain. Math. J. 2019, 71 (2), 308-321.
doi: 10.1007/s11253-019-01646-3
(translation of Ukrain. Mat. Zh. 2019, 71 (2), 271-282. (in Ukrainian))
-
Romanyuk A.S., Romanyuk V.S.
Estimation of Some Approximating Characteristics of the Classes of Periodic Functions of One and Many Variables.
Ukrain. Math. J. 2020, 71 (8), 1257-1272.
doi: 10.1007/s11253-019-01711-x
(translation of Ukrain. Mat. Zh. 2019, 71 (8), 1102-1115. (in Ukrainian))
-
Stasyuk S.A.
Approximation of the Classes $B^{\Omega}_{p,\theta}$ of Periodic Functions of Many Variables in Uniform Metric.
Ukrain. Math. J. 2002, 54 (11), 1885-1896.
doi: 10.1023/A:1024000709997
(translation of Ukrain. Mat. Zh. 2002, 54 (11), 1551-1554. (in Ukrainian))
-
Stasyuk S.A., Fedunyk O.V.
Approximation characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of many variables.
Ukrain. Math. J. 2006, 58 (5), 779-793.
doi: 10.1007/s11253-006-0101-x
(translation of Ukrain. Mat. Zh. 2006, 58 (5), 692-704. (in Ukrainian))
-
Stechkin S.B.
On the order of the best approximations of continuous functions.
Izv. Ross. Akad. Nauk Ser. Mat. 1951, 15 (3) 219-242. (in Russian)
-
Temlyakov V.N.
Approximation of functions with bounded mixed derivative.
Proc. Steklov Inst. Math. 1989, 178, 1-121.
(translation of Tr. Mat. Inst. Steklova 1986, 178, 3-113. (in Russian))
-
Temlyakov V.N.
Approximation of Periodic Functions.
Nova Science Publishers, Inc., New York, 1993.
-
Temlyakov V.N.
Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions.
Izv. Math. 1986, 27 (2), 285-322.
doi: 10.1070/IM1986v027n02ABEH001179
(translation of Izv. Ross. Akad. Nauk Ser. Mat. 1985, 49 (5), 986-1030. (in Russian))
-
Temlyakov V.N.
Diameters of some classes of functions of several variables.
Dokl. Akad. Nauk 1982, 267 (2), 314-317. (in Russian)
-
Temlyakov V.N.
Estimates of the asymptotic characteristics of classes of functions with bounded mixed derivative or difference.
Proc. Steklov Inst. Math. 1990, 189, 161-197.
(translation of Tr. Mat. Inst. Steklova 1989, 189, 138-168. (in Russian))
-
Yongsheng S., Heping W.
Representation and approximation of multivariate periodic functions with bounded mixed moduli of smoothness.
Tr. Mat. Inst. Steklova 1997, 219, 356-377.