01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
22.02.1952
E-mail:
Keywords:
multiple trigonometrical Fourier series, Fourier orthogonal polynomial series; estimations of weight norms of maximal operators; methods of mathematics.
Subject:
The problems of convergence and summability of multiple trigonometrical Fourier series and Fourier–Jacobi series over parallelepipeds and simplexes are investigated . Some multi-dimensional analog of their equiconvergence and the loss of a classical equiconvergence are proved. The behaviour of linear means inside and on boundary of domain of orthogonality is investigated.
Biography
Graduated from Faculty of physics and mathematics of Tambov State Pedagogical Institute in 1973. Ph.D. thesis was defended in 1985. A list of my works contains more than 70 titles.
Main publications:
Nakhman A. D. Obobschennaya zadacha Dirikhle s granichnoi funktsiei iz klassa $L_{\nu}^p$ // Differents. uravneniya, 1990, t. 26, # 8, s. 1375–1382.
Nakhman A. D. Srednie tipa Martsinkevicha polinomialnykh razlozhenii Fure // Dokl. AN SSSR, 1991, t. 321, # 3, s. 474–477.
Nakhman A. D. O chastnykh sumakh kratnykh ryadov Fure po mnogochlenam Yakobi // Izv. vuzov. Matem., 1999, # 3, s. 46–56.
Nakhman A. D. Konstanty Lebega srednikh arifmeticheskikh dvoinykh summ Fure–Lezhandra // Izv. vuzov. Matem., 1999, # 8, s. 37–46.
Kulikov G. M., Nakhman A. D. Metod Fure v uravneniyakh matematicheskoi fiziki. M., Mashinostroenie, 2000, 155 s.
A. D. Nakhman, “Limit behavior of generalized de la Vallée-Poussin sums of multiple Fourier series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 9, 38–51; Russian Math. (Iz. VUZ), 49:9 (2005), 36–48
1999
2.
A. D. Nakhman, “Lebesgue constants of arithmetic means of double Fourier–Legendre sums”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 8, 37–46; Russian Math. (Iz. VUZ), 43:8 (1999), 34–43
3.
A. D. Nakhman, “On partial sums of multiple Fourier series in Jacobi polynomials”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 3, 46–56; Russian Math. (Iz. VUZ), 43:3 (1999), 44–55
1991
4.
A. D. Nakhman, “Marcinkiewicz-type means of polynomial Fourier expansions”, Dokl. Akad. Nauk SSSR, 321:3 (1991), 474–477; Dokl. Math., 44:3 (1992), 726–729
5.
A. D. Nakhman, “Summation of Fourier expansions in systems of polynomial form”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 3, 35–47; Soviet Math. (Iz. VUZ), 35:3 (1991), 33–43
1990
6.
A. D. Nakhman, “The generalized Dirichlet problem with a boundary function in the class $L_\nu^p$”, Differ. Uravn., 26:8 (1990), 1375–1382; Differ. Equ., 26:8 (1990), 1012–1018
7.
A. D. Nakhman, “Generalized de la Valleé–Poussin means for multiple Fourier series”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 1, 61–69; Soviet Math. (Iz. VUZ), 34:1 (1990), 71–80
A. D. Nakhman, “Theorems of Rosenblum–Muckenhoupt type for multiple Fourier series of vector-valued functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1984, no. 4, 25–31; Soviet Math. (Iz. VUZ), 28:4 (1984), 31–39
A. D. Nakhman, B. P. Osilenker, “Estimates of weighted norms of some operators generated by multiple trigonometric Fourier series”, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 4, 39–50; Soviet Math. (Iz. VUZ), 26:4 (1982), 46–59
A. D. Nakhman, B. P. Osilenker, “Some linear convergent processes that are generated by periodic functions of two variables”, Izv. Vyssh. Uchebn. Zaved. Mat., 1976, no. 10, 105–108; Soviet Math. (Iz. VUZ), 20:10 (1976), 85–87
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