Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
10.11.1924
Website: https://www.mathnet.ru/rus/rm9201 Keywords: Best approximation in Banach spaces; duality theorems for best approximation; conditions of existance and uniqueness of best approximation; geometry of a Banach sphere; Chebyshev systems; Chebyshev centre; approximation in the spaces of continuous and summables functions; approximation of functions of several variables; superpositions of functions.
Subject:
The following results are obtained: on simultaneous approximation of a function with its derivatives; on criterion of best approximation; duality theorems of convex approximation; conditions of existance and uniqueness of best approximation in general Banach spaces, in Frechet spaces and in spaces of continued and summable functions; on conditions of existance and uniqueness of Chebyshev centre; on the best approximation of functions of several variables by linear superpositions; on optimization of building process with random parameters.
Main publications:
Garkavi A. L. On the problem of best approximation of a function $f(x,y)$ by sums $\phi(ax+by)+\psi(cx+dy)$ // East J. Approximation, 1996, 2 (2), 151–154.
