There are proved the necessary and sufficient conditions on absolute convergence of Fourier series with respect to generalized Haar systems; sufficient conditions of the absolute summability of multiple trigonometric Fourier series function in Lebesque spaces in terms of modules of smoothness and the best approximation.
Biography
Graduated from Faculty of Mathematics of Karaganda State University in 1977 (department of mathematical analysis). Ph.D. thesis was defended in 1983. A list of my works contains more than 50 titles.
Main publications:
Akishev G. O nekotorykh teoremakh dlya sistemy Praisa // Izv. vuzov, seriya matem., 2002 g., # 1, s. 3–8.
Akishev G., Makhashev S. T. Ob absolyutnoi skhodimosti ryadov Fure po obobschennoi sisteme Khaara // Izv. vuzov, 2000 g., # 3, s. 3–11.
Akishev G., Askarova A. Zh. Ob usloviyakh skhodimosti ryadov iz koeffitsientov Fure funktsii mnogikh peremennykh // Izv. Tulskogo gosuniversiteta, 1998, t. 4, # 3, s. 5–11.
Akishev G. O vlozhenii nekotorykh klassov funktsii mnogikh peremennykh v prostranstvo Lorentsa // Izv. AN KazSSR, ser. fiz.-matem., 1982, # 3.
G. Akishev, “Estimates of $M$–term approximations of functions of several variables in the Lorentz space by a constructive method”, Eurasian Math. J., 15:2 (2024), 8–32
2023
2.
G. A. Akishev, “Inequalities for the best “angular” approximation and the smoothness modulus of a function in the Lorentz space”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 230 (2023), 8–24
3.
G. A. Akishev, “On orders of $n$-term approximations of functions of many variables in the Lorentz space”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 227 (2023), 3–19
4.
G. Akishev, “On estimates of the order of the best $M$-term approximations of functions of several variables in the anisotropic Lorentz – Zygmund space”, Izv. Saratov Univ. Math. Mech. Inform., 23:2 (2023), 142–156
5.
G. A. Akishev, “Nikol'skii's inequality of different metrics for trigonometric polynomials in a space with mixed asymmetric norm”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:4 (2023), 11–26
G. A. Akishev, “On estimates for orders of best $M$-term approximations
of multivariate functions in anisotropic Lorentz–Karamata spaces”, Ufimsk. Mat. Zh., 15:1 (2023), 3–21; Ufa Math. J., 15:1 (2023), 1–20
2022
7.
G. A. Akishev, “On estimates of linear widths for classes of multivariate functions in the Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022), 23–39
8.
G. A. Akishev, “On the best M-term approximations of functions from the Nikol'skii-Besov class in the Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:1 (2022), 7–26
2020
9.
G. A. Akishev, “Estimates for the best approximations of functions from the Nikol'skii-Besov class in the Lorentz space by trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:2 (2020), 5–27
Gabdolla Akishev, “Estimates of best approximations of functions with logarithmic smoothness in the Lorentz space with anisotropic norm”, Ural Math. J., 6:1 (2020), 16–29
2019
11.
G. A. Akishev, “On the exactness of the inequality of different metrics for trigonometric polynomials in the generalized Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:2 (2019), 9–20
G. A. Akishev, “Estimates for best approximations of functions from the logarithmic smoothness class in the Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:3 (2017), 3–21
G. A. Akishev, “On approximation orders of functions of several variables in the Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:4 (2016), 13–28; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 9–24
G. A. Akishev, “Estimates for Kolmogorov widths of the Nikol'skii — Besov — Amanov classes in the Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:4 (2015), 3–13; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 1–12
2010
16.
G. A. Akishev, “On the exact estimations of the best $M$–terms approximation of the Besov class”, Sib. Èlektron. Mat. Izv., 7 (2010), 255–274
G. A. Akishev, “Absolute convergence of Fourier series of superpositions of functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 11, 3–11; Russian Math. (Iz. VUZ), 53:11 (2009), 1–8
18.
G. A. Akishev, “The ortho-diameters of Nikol'skii and Besov classes in the Lorentz spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 2, 25–33; Russian Math. (Iz. VUZ), 53:2 (2009), 21–29
G. A. Akishev, “Convergence of Double Fourier Series of Functions from Symmetric Spaces”, Mat. Zametki, 81:3 (2007), 323–327; Math. Notes, 81:3 (2007), 287–290
21.
G. A. Akishev, “On Orders of Approximation of Function Classes in Lorentz spaces with Anisotropic Norm”, Mat. Zametki, 81:1 (2007), 3–16; Math. Notes, 81:1 (2007), 3–14
G. A. Akishev, “On degrees of approximation of some classes by polynomials with respect to generalized Haar system”, Sib. Èlektron. Mat. Izv., 3 (2006), 92–105
G. Akishev, “On degree of approximation function classes in the space Lebesgue with anisotropic norm”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148:2 (2006), 5–17
G. A. Akishev, “On orders of approximation of function classes by polynomials in the generalized Haar system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 3, 13–22; Russian Math. (Iz. VUZ), 2005, no. 3, 11–20
G. A. Akishev, “On some theorems for the Price system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 1, 3–8; Russian Math. (Iz. VUZ), 46:1 (2002), 1–6
2000
28.
G. A. Akishev, S. T. Makhashev, “On the absolute convergence of Fourier series in the generalized Haar system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2000, no. 3, 8–16; Russian Math. (Iz. VUZ), 44:3 (2000), 6–14
2009
29.
G. A. Akishev, “Corrections to the paper “Generalized Haar system and theorems of embedding into symmetrical spaces” (Fundamentalnaya i Prikladnaya Matematika, Vol. 8, No. 2, 319–334 (2002))”, Fundam. Prikl. Mat., 15:5 (2009), 209–210
2008
30.
G. A. Akishev, “Erratum to “On degree of approximation of classes polynomials with respect to generalized Haar system””, Sib. Èlektron. Mat. Izv., 5 (2008), 383–386
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