approximation of functions; integral equations; approximation of solutions of an operator equations.
Subject:
The intervals of uniform convergence of Newton–Kantorovich's method for nonlinear Volterra integral equations of second genus in Banach space were investigated. The issues of approximation functions of bounded Hardy's variation in the space $C(R^2)$ by means of shifts and dilations of one function were investigated (with V. V. Zhuk). The exact inequalities for the modulus of continuity of functions of several variables were established.
Biography
Graduated from Faculty of Mathematics and Mechanics of St. Petersburg State University (SPbSU) in 1977 (Department of mathematical analysis). Ph. D. thesis was defended in 1998. A list of my works contains more than 20 titles.
Main publications:
Dodonov N. Yu., Zhuk V. V. On approximation of functions of bounded variation in the space $C(R^2)$ by means of shifts and dilations of one function // International conference OFEA'2001, Russia, St. Petersburg, June 25–29, 2001, 127–128.
N. Yu. Dodonov, V. V. Zhuk, “On approximating periodic functions by Riesz sums”, Zap. Nauchn. Sem. POMI, 371 (2009), 18–36; J. Math. Sci. (N. Y.), 166:2 (2010), 134–144
2006
2.
N. Yu. Dodonov, V. V. Zhuk, “On approximating periodic functions by singular integrals with positive kernels”, Zap. Nauchn. Sem. POMI, 337 (2006), 51–72; J. Math. Sci. (N. Y.), 143:3 (2007), 3039–3052
2004
3.
V. M. Babich, A. M. Vershik, V. S. Videnskii, O. L. Vinogradov, I. K. Daugavet, N. Yu. Dodonov, V. V. Zhuk, B. M. Makarov, A. N. Podkorutov, Yu. G. Reshetnyak, M. A. Skopina, V. L. Fainshmidt, V. P. Havin, N. A. Shirokov, “Garal'd Isidorovich Natanson (obituary)”, Uspekhi Mat. Nauk, 59:4(358) (2004), 181–185; Russian Math. Surveys, 59:4 (2004), 771–776
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