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Garkavi, Alexander Lwowich

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Total publications: 41
Scientific articles: 40

Number of views:
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Abstract pages:6913
Full texts:2852
References:142
Doctor of physico-mathematical sciences (1966)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 10.11.1924
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.

Biography

Graduated from Lwow University in 1956 and post-graduate course in Moscow Mathem. Steklov Institute (MIAN) in 1959 (department of theory of function and fuctional analysis). Ph.D. thesis was defended in 1960. D.Sci. thesis was defended in 1966. A list of my works contains more than 90 titles.

   
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.

http://www.mathnet.ru/eng/person8429
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/196642

Publications in Math-Net.Ru
1997
1. A. L. Garkavi, “On the approximation of functions in two variables by sums of the form $\varphi (x)+\psi (y)$ in the spaces $L_p$ ($1\le p\le \infty $)”, Sibirsk. Mat. Zh., 38:1 (1997),  56–68  mathnet  mathscinet  zmath; Siberian Math. J., 38:1 (1997), 47–57  isi
2. A. L. Garkavi, “On Existence of Best Approximation of a Function of Two Variables by Sums of Plane Waves”, Tr. Mat. Inst. Steklova, 219 (1997),  130–136  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 219 (1997), 123–129
1996
3. A. L. Garkavi, V. A. Medvedev, S. Ya. Havinson, “Existence of the best possible uniform approximation of a function of several variables by a sum of functions of fewer variables”, Mat. Sb., 187:5 (1996),  3–14  mathnet  mathscinet  zmath; Sb. Math., 187:5 (1996), 623–634  isi  scopus
1995
4. A. L. Garkavi, V. A. Medvedev, S. Ya. Havinson, “On existence of a best uniform approximation of a function in two variables by the sums $\varphi(x)+\psi(y)$”, Sibirsk. Mat. Zh., 36:4 (1995),  819–827  mathnet  mathscinet  zmath; Siberian Math. J., 36:4 (1995), 707–713  isi
1993
5. A. L. Garkavi, “On minimization of integral functionals on the space of measurable functions”, Mat. Zametki, 54:5 (1993),  13–22  mathnet  mathscinet  zmath  elib; Math. Notes, 54:5 (1993), 1093–1099  isi
1990
6. A. L. Garkavi, V. A. Kaminskii, “Certain extremal problem in a measure space”, Mat. Zametki, 48:4 (1990),  19–28  mathnet  mathscinet  zmath; Math. Notes, 48:4 (1990), 985–991  isi
1989
7. A. L. Garkavi, “Haar's condition for systems of vector-valued functions”, Mat. Zametki, 45:1 (1989),  10–15  mathnet  mathscinet  zmath; Math. Notes, 45:1 (1989), 7–11  isi
1986
8. A. L. Garkavi, “Uniqueness of the best approximation in mean of vector-valued functions”, Mat. Zametki, 39:3 (1986),  337–348  mathnet  mathscinet  zmath; Math. Notes, 39:3 (1986), 183–189  isi
1985
9. A. L. Garkavi, V. A. Shmatkov, “Uniqueness of a continuation of positive functionals”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, 9,  10–14  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 29:9 (1985), 10–15
1983
10. A. L. Garkavi, “Estimating the norm of a conditional extension of a linear functional”, Mat. Zametki, 34:4 (1983),  559–572  mathnet  mathscinet  zmath; Math. Notes, 34:4 (1983), 769–775  isi
1981
11. A. L. Garkavi, “Minimax balayage theorem and an inscribed ball problem”, Mat. Zametki, 30:1 (1981),  109–121  mathnet  mathscinet  zmath; Math. Notes, 30:1 (1981), 542–548  isi
1980
12. A. L. Garkavi, “Method of cyclic descent in the problem of best approximation”, Mat. Zametki, 27:4 (1980),  549–558  mathnet  mathscinet  zmath; Math. Notes, 27:4 (1980), 270–274  isi
1978
13. A. L. Garkavi, V. B. Gogolevskii, “On reliability of multicomputer systems”, Avtomat. i Telemekh., 1978, 4,  161–168  mathnet  zmath
1975
14. A. L. Garkavi, V. N. Zamyatin, “Conditional Chebyshev center of a bounded set of continuous functions”, Mat. Zametki, 18:1 (1975),  67–76  mathnet  mathscinet  zmath; Math. Notes, 18:1 (1975), 622–627
1974
15. A. L. Garkavi, V. A. Shmatkov, “On the Lamé point and its generalizations in a normed space”, Mat. Sb. (N.S.), 95(137):2(10) (1974),  272–293  mathnet  mathscinet  zmath; Math. USSR-Sb., 24:2 (1974), 267–286
1973
16. A. L. Garkavi, “The conditional Chebyshev center of a compact set of continuous functions”, Mat. Zametki, 14:4 (1973),  469–478  mathnet  mathscinet  zmath; Math. Notes, 14:4 (1973), 827–831
1972
17. A. L. Garkavi, “A certain criterion for a $K$-system of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, 4,  55–59  mathnet  mathscinet  zmath
1971
18. A. L. Garkavi, “The Helly problem and best approximation of summable functions”, Mat. Sb. (N.S.), 84(126):2 (1971),  196–217  mathnet  zmath; Math. USSR-Sb., 13:2 (1971), 187–207
1970
19. A. L. Garkavi, “The existence of a best approximating element in $(F)$-space with integral metric”, Mat. Zametki, 8:5 (1970),  583–594  mathnet  mathscinet  zmath; Math. Notes, 8:5 (1970), 797–802
20. A. L. Garkavi, “Characteristic of Chebyshev subspaces of finite codimension in $L_1$”, Mat. Zametki, 7:2 (1970),  155–163  mathnet  mathscinet  zmath; Math. Notes, 7:2 (1970), 95–99
1969
21. A. L. Garkavi, “The theory of best approximation in normed linear spaces”, Itogi Nauki. Ser. Matematika. Mat. Anal. 1967, 1969,  75–132  mathnet  mathscinet  zmath; Progr. Math., 8 (1970), 83–150
1967
22. A. L. Garkavi, “The Helly problem and best approximation in a space of continuous functions”, Izv. Akad. Nauk SSSR Ser. Mat., 31:3 (1967),  641–656  mathnet  mathscinet  zmath; Math. USSR-Izv., 1:3 (1967), 623–637
23. A. L. Garkavi, A. M. Flomin, “Approximative properties of sets in certain topological spaces”, Mat. Zametki, 2:5 (1967),  523–530  mathnet  mathscinet  zmath; Math. Notes, 2:5 (1967), 809–812
24. A. L. Garkavi, “The unit sphere of the space of polynomials with integral metric”, Mat. Zametki, 1:3 (1967),  299–304  mathnet  mathscinet  zmath; Math. Notes, 1:3 (1967), 199–202
25. A. L. Garkavi, “On compacta admitting Chebyshev systems of measures”, Mat. Sb. (N.S.), 74(116):2 (1967),  209–217  mathnet  mathscinet  zmath; Math. USSR-Sb., 3:2 (1967), 195–203
1965
26. A. L. Garkavi, “Almost-Chebyshev systems of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1965, 2,  36–44  mathnet  mathscinet  zmath
1964
27. A. L. Garkavi, “Approximation properties of subspaces of finite defect in the space of continuous functions”, Dokl. Akad. Nauk SSSR, 155:3 (1964),  513–516  mathnet  mathscinet  zmath
28. A. L. Garkavi, “On Chebyshev and almost-Chebyshev subspaces”, Izv. Akad. Nauk SSSR Ser. Mat., 28:4 (1964),  799–818  mathnet  mathscinet  zmath
29. A. L. Garkavi, “On the uniqueness of the $L$-problem of moments”, Izv. Akad. Nauk SSSR Ser. Mat., 28:3 (1964),  553–570  mathnet  mathscinet  zmath
30. A. L. Garkavi, “On the Chebyshev center and convex hull of a set”, Uspekhi Mat. Nauk, 19:6(120) (1964),  139–145  mathnet  mathscinet  zmath
1963
31. A. L. Garkavi, “On Chebyshev and almost-Chebyshev subspaces”, Dokl. Akad. Nauk SSSR, 149:6 (1963),  1250–1252  mathnet  mathscinet  zmath
32. A. L. Garkavi, “A topology in Banach spaces”, Uspekhi Mat. Nauk, 18:1(109) (1963),  151–154  mathnet  mathscinet  zmath
33. A. L. Garkavi, “On best approximation by the elements of infinite-dimensional subspaces of a certain class”, Mat. Sb. (N.S.), 62(104):1 (1963),  104–120  mathnet  mathscinet  zmath
1962
34. A. L. Garkavi, “On the optimal net and best cross-section of a set in a normed space”, Izv. Akad. Nauk SSSR Ser. Mat., 26:1 (1962),  87–106  mathnet  mathscinet  zmath
35. A. L. Garkavi, “Chebyshev and almost Chebyshev subspaces”, Uspekhi Mat. Nauk, 17:5(107) (1962),  195–196  mathnet
1961
36. A. L. Garkavi, “Duality theorems for approximation by elements of convex sets”, Uspekhi Mat. Nauk, 16:4(100) (1961),  141–145  mathnet  mathscinet  zmath
1960
37. A. L. Garkavi, “On the spaces of linear operators”, Dokl. Akad. Nauk SSSR, 132:3 (1960),  497–500  mathnet  mathscinet  zmath
38. A. L. Garkavi, “Simultaneous approximation to a periodic function and its derivatives by trigonometric polynomials”, Izv. Akad. Nauk SSSR Ser. Mat., 24:1 (1960),  103–128  mathnet  mathscinet  zmath
39. A. L. Garkavi, “Existence of the best net and the best width for set in a Banach space”, Uspekhi Mat. Nauk, 15:2(92) (1960),  210–211  mathnet
1959
40. A. L. Garkavi, “Dimensionality of polyhedra of best approximation for differentiable functions”, Izv. Akad. Nauk SSSR Ser. Mat., 23:1 (1959),  93–114  mathnet  mathscinet  zmath

1958
41. A. L. Garkavi, “Correction”, Uspekhi Mat. Nauk, 13:3(81) (1958),  254  mathnet

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