01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
04.04.1945
E-mail:
Keywords:
functions of generalized bounded variation; Fourier analysis; interpolation; approximation of functions.
Subject:
The notation of function of (m,Ô)-bounded variation is introduced. This notation contains as particulary cases different generalizations of notation of function of bounded variation which were suggested by different authors earlier. The properties of functions of this class, in particularity, behavior of Fourier series and Lagrange trigonometric interpolation of these functions are investigated.
Biography
Graduated from Faculty of Mathematics and Mechanics of Leningrad State University in 1968. Ph.D. thesis was defended in 1980. A list of my papers contains more than 30 papers.
Main publications:
Kelzon A. A. O funktsiyakh (m,F)-ogranichennoi variatsii // DAN. 1991. 321(4). 670–672.
Kelzon A. A. Tochnye otsenki koeffitsientov Fure–Lagranzha funktsii ogranichennoi variatsii // Matem. zametki. 1993. 53(6). 52–62.
Kelzon A. A. Funktsii (m,F)-ogranichennoi variatsii i skhodimost ryadov Fure // Izvestiya vuzov. Matem. 1994. 8. 29–38.
Kelzon A. A. O trigonometricheskom interpolirovanii funktsii m-garmonicheskoi ogranichennoi variatsii // Izvestiya vuzov. Matem. 1997. 10. 44–47.
Kelzon A. A. Otsenka pogreshnosti trigonometricheskogo interpolirovaniya funktsii m-garmonicheskoi ogranichennoi variatsii // Izvestiya vuzov. Matem. 2001. 1. 49–54.
A. A. Kelzon, “Determination of the jump of a function of $m$-harmonic bounded variation by its Fourier series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 5, 41–47
2016
2.
A. A. Kelzon, “Determination of the Jump of a Function of Generalized Bounded Variation from the Derivatives of the Partial Sums of Its Fourier Series”, Mat. Zametki, 99:1 (2016), 35–41; Math. Notes, 99:1 (2016), 46–51
A. A. Kelzon, “Determination of the Jump of a Function of Generalized Bounded Variation by the Derivatives of a Trigonometric Interpolation Polynomial”, Mat. Zametki, 76:1 (2004), 78–86; Math. Notes, 76:1 (2004), 73–80
2001
4.
A. A. Kelzon, “An error estimate for the trigonometric interpolation of functions of $m$-harmonic bounded variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 1, 49–54; Russian Math. (Iz. VUZ), 45:1 (2001), 46–51
1997
5.
A. A. Kelzon, “Trigonometric interpolation of functions of $m$-harmonic bounded variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1997, no. 10, 44–47; Russian Math. (Iz. VUZ), 41:10 (1997), 42–45
A. A. Kelzon, “Functions of $(m,\Phi)$-bounded variation and the convergence of Fourier series”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, no. 8, 29–38; Russian Math. (Iz. VUZ), 38:8 (1994), 28–37
A. A. Kelzon, “Sharp estimates of Fourier–Lagrange coefficients of functions of bounded variation”, Mat. Zametki, 53:6 (1993), 52–62; Math. Notes, 53:6 (1993), 597–604
1992
8.
A. A. Kelzon, “Fourier and Fourier-Lagrange coefficients of functions of $(m,\lambda)$-bounded variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, no. 9, 59–64; Russian Math. (Iz. VUZ), 36:9 (1992), 55–60
1991
9.
A. A. Kelzon, “Functions of $(m,\Phi)$-bounded variation”, Dokl. Akad. Nauk SSSR, 321:4 (1991), 670–672; Dokl. Math., 44:3 (1992), 768–770
A. A. Kelzon, “Study of Lagrange interpolation processes under a change in the system of nodes”, Izv. Vyssh. Uchebn. Zaved. Mat., 1976, no. 4, 126–129; Soviet Math. (Iz. VUZ), 20:4 (1976), 110–114
1975
16.
A. A. Kelzon, “On the Fourier coefficients and Fourier–Lagrange coefficients of functions of bounded higher variations”, Dokl. Akad. Nauk SSSR, 221:2 (1975), 283–286
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