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Garkavi, Alexander Lwowich
(1924–2007)
Statistics Math-Net.Ru
Total publications: 43
Scientific articles: 42

Number of views:
This page:1178
Abstract pages:12541
Full texts:7202
References:300
Professor
Doctor of physico-mathematical sciences (1966)
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.

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.

https://www.mathnet.ru/eng/person8429
https://ru.wikipedia.org/wiki/Garkavi,_Aleksandr_Lvovich
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/196642

Publications in Math-Net.Ru Citations
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”, Trudy Mat. Inst. Steklova, 219 (1997),  130–136  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 219 (1997), 123–129 2
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 3
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 8
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
7. A. L. Garkavi, “Algebraic and geometric components of Chebyshev rank of a system of vector-valued functions”, Sibirsk. Mat. Zh., 31:6 (1990),  39–45  mathnet  mathscinet  zmath; Siberian Math. J., 31:6 (1990), 904–909  isi 2
1989
8. 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 3
1986
9. 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
10. A. L. Garkavi, V. A. Shmatkov, “Uniqueness of a continuation of positive functionals”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, no. 9,  10–14  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 29:9 (1985), 10–15
1983
11. 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
12. 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
13. 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 5
1978
14. A. L. Garkavi, V. B. Gogolevskii, “On reliability of multicomputer systems”, Avtomat. i Telemekh., 1978, no. 4,  161–168  mathnet  zmath
1975
15. 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 9
1974
16. 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 13
1973
17. 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 8
1972
18. A. L. Garkavi, “A certain criterion for a $K$-system of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 4,  55–59  mathnet  mathscinet  zmath
1971
19. 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 1
1970
20. 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 6
21. 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 1
1969
22. 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 13
1967
23. 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 5
24. 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
25. 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 1
26. 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 3
1965
27. A. L. Garkavi, “Almost-Chebyshev systems of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1965, no. 2,  36–44  mathnet  mathscinet  zmath 1
1964
28. 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 2
29. A. L. Garkavi, “On Chebyshev and almost-Chebyshev subspaces”, Izv. Akad. Nauk SSSR Ser. Mat., 28:4 (1964),  799–818  mathnet  mathscinet  zmath 3
30. 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 3
31. 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 32
32. A. L. Garkavi, “A criterion for the element of best approximation”, Sibirsk. Mat. Zh., 5:2 (1964),  472–476  mathnet  mathscinet  zmath 3
1963
33. A. L. Garkavi, “On Chebyshev and almost-Chebyshev subspaces”, Dokl. Akad. Nauk SSSR, 149:6 (1963),  1250–1252  mathnet  mathscinet  zmath 1
34. A. L. Garkavi, “A topology in Banach spaces”, Uspekhi Mat. Nauk, 18:1(109) (1963),  151–154  mathnet  mathscinet  zmath
35. 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 6
1962
36. 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 23
37. A. L. Garkavi, “Chebyshev and almost Chebyshev subspaces”, Uspekhi Mat. Nauk, 17:5(107) (1962),  195–196  mathnet
1961
38. A. L. Garkavi, “Duality theorems for approximation by elements of convex sets”, Uspekhi Mat. Nauk, 16:4(100) (1961),  141–145  mathnet  mathscinet  zmath 5
1960
39. A. L. Garkavi, “On the spaces of linear operators”, Dokl. Akad. Nauk SSSR, 132:3 (1960),  497–500  mathnet  mathscinet  zmath
40. 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 8
41. 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 9
1959
42. 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
43. A. L. Garkavi, “Correction”, Uspekhi Mat. Nauk, 13:3(81) (1958),  254  mathnet

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