Persons: Alimov, Alexey Rostislavovich

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Alimov, Alexey Rostislavovich

Statistics
in MathSciNet:	57 (55)
in zbMATH:	47 (45)
in Web of Science:	54 (53)
in Scopus:	49 (49)

Head Scientist Researcher

Doctor of physico-mathematical sciences (2015)

Speciality:

01.01.01 (Real analysis, complex analysis, and functional analysis)

Birth date:

31.08.1971

E-mail:

Keywords:

best approximation, Chebyshev set, sun, strict sun.

UDC:

517.982.272, 517.982.256, 517.982, 517.982.252

MSC:

41A65, 41A65

Subject:

Theory of approximations in normed linear spaces.

Main publications:

A. R. Alimov, Sokhranenie approksimativnykh svoistv podmnozhestv chebyshevskikh mnozhestv i solnts v $\ell^\infty(n)$. Izv. RAN. Ser. matem., 2006, 70:5, 3–12.
A. R. Alimov, Monotonnaya lineinaya svyaznost chebyshevskikh mnozhestv v prostranstve $C(Q)$. Matem. sb., 2006, 197:9, 3–18.
A. R. Alimov, Geometricheskoe stroenie chebyshevskikh mnozhestv v $\ell^\infty(n)$. Funkts. analiz i ego pril., 2005, 39:1, 1–10.
A. R. Alimov, Svyaznost solnts v prostranstve $c_0$. Izv. RAN. Ser. matem., 2005, 69:4, 3–18.
A. R. Alimov, O strukture dopolneniya k chebyshevskim mnozhestvam. Funkts. analiz i ego pril., 2001, 35:3, 19–27.

https://www.mathnet.ru/eng/person13059

List of publications on Google Scholar

https://zbmath.org/authors/ai:alimov.alexey-r

https://mathscinet.ams.org/mathscinet/MRAuthorID/602442

https://elibrary.ru/author_items.asp?authorid=14681

ISTINA

https://istina.msu.ru/workers/3628613

https://orcid.org/0000-0001-8806-1593

https://www.webofscience.com/wos/author/record/M-3902-2015

https://www.scopus.com/authid/detail.url?authorId=7007117638

https://www.researchgate.net/profile/A_Alimov

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
2.	Alexey R. Alimov, Igor' G. Tsarkov, Geometric Approximation Theory, Springer Monographs in Mathematics, Springer, 2022 , xxi+508 pp.	37 ^[x]
3.	A. R. Alimov, “On the Structure of the Complements of Chebyshev Sets”, Funct. Anal. Appl., 35:3 (2001), 176–182
4.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
5.	A. R. Alimov, “Monotone path-connectedness of Chebyshev sets in the space $C(Q)$”, Sb. Math., 197:9 (2006), 1259–1272
6.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
7.	A. R. Alimov, “Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces”, Izv. Math., 78:4 (2014), 641–655
8.	Alexey R. Alimov, Igor' G. Tsar'kov, “Suns, moons, and $\mathring B$-complete sets in asymmetric spaces”, Set-Valued Var. Anal., 30 (2022), 1233–1245	24 ^[x]
9.	A. R. Alimov, “The Banach–Mazur theorem for spaces with an asymmetric distance”, Russian Math. Surveys, 58:2 (2003), 367–369
10.	Alexey R. Alimov, Igor' G. Tsar'kov, “Ball-complete sets and solar properties of sets in asymmetric spaces”, Result. Math., 77 (2022), 86	22 ^[x]
11.	A. R. Alimov, I. G. Tsarkov, “$\overset{\circ}B$-complete sets: approximative and structural properties”, Siberian Math. J., 63 (2022), 412–420
12.	A. R. Alimov, “Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(2) (2014), 489–497
13.	A. R. Alimov, “Connectedness of suns in the space $c_0$”, Izv. Math., 69:4 (2005), 651–666
14.	A. R. Alimov, I. G. Tsar'kov, “Solarity and proximinality in generalized rational approximation in spaces C(Q) and Lp”, Russian Journal of Mathematical Physics, 29:3 (2022), 291-305	15 ^[x]
15.	A. R. Alimov, “Strict Protosuns in Asymmetric Spaces of Continuous Functions”, Results in Mathematics, 78 (2023), 95 , 15 pp.	12 ^[x]
16.	A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928
17.	A. R. Alimov, “The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$”, Funct. Anal. Appl., 39:1 (2005), 1–8
18.	A. R Alimov, “Monotone path-connectedness of strict suns”, Lobachevskii Journal of Mathematics, 43:3 (2022), 519–-527	10 ^[x]
19.	A. R. Alimov, B. B. Bednov, “Monotone path-connectedness of Chebyshev sets in three-dimensional spaces”, Sb. Math., 212:5 (2021), 636–654
20.	A. R. Alimov, I. G. Tsar'kov, “Smoothness of subspace sections of the unit balls of $C(Q)$ and $L^1$”, J. Approx. Theory, 65 (2021), 105552 , 8 pp.	10 ^[x]
21.	A. R. Alimov, “Geometrical Characterization of Strict Suns in $\ell^\infty(n)$”, Math. Notes, 70:1 (2001), 3–10
22.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev unions of planes, and their approximative and geometric properties”, J. Approx. Theory, 298 (2024), 106009 , 12 pp.	9 ^[x]
23.	A. R. Alimov, K. S. Ryutin, I. G. Tsar'kov, “Existence, uniqueness, and stability of best and near-best approximations”, Russian Math. Surveys, 78:3 (2023), 399–442
24.	A. R. Alimov, I. G. Tsar'kov, “Approximatively Compact Sets in Asymmetric Efimov–Stechkin Spaces and Convexity of Almost Suns”, Math. Notes, 110:6 (2021), 947–951
25.	A. R. Alimov, E. V. Shchepin, “Convexity of Chebyshev sets with respect to tangent directions”, Russian Math. Surveys, 73:2 (2018), 366–368
26.	A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454
27.	A. R. Alimov, V. Yu. Protasov, “Separation of convex sets by extreme hyperplanes”, J. Math. Sci., 191:5 (2013), 599–604
28.	A. R. Alimov, “A Monotone Path Connected Chebyshev Set Is a Sun”, Math. Notes, 91:2 (2012), 290–292
29.	A. R. Alimov, “Vypuklost i monotonnaya lineinaya svyaznost mnozhestv s nepreryvnoi metricheskoi proektsiei v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 26:2 (2020), 28-46	8 ^[x]
30.	A. R. Alimov, “Preservation of approximative properties of subsets of Chebyshev sets and suns in $\ell^\infty (n)$”, Izv. Math., 70:5 (2006), 857–866
31.	A. R. Alimov, “Convexity of Chebyshev Sets Contained in a Subspace”, Math. Notes, 78:1 (2005), 3–13
32.	A. R. Alimov, I. G. Tsar'kov, “Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces”, Math. Notes, 112:1 (2022), 3–16
33.	A. R. Alimov, “Sokhranenie approksimativnykh svoistv chebyshëvskikh mnozhestv i solnts na ploskosti”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 63:4 (2008), 46–49	7 ^[x]
34.	A. R. Alimov, “Characterisations of Chebyshev sets in $c_0$”, J. Approx. Theory, 129:2 (2004), 217–229	7 ^[x]
35.	A. R. Alimov, M. I. Karlov, “Sets with External Chebyshev Layer”, Math. Notes, 69:2 (2001), 269–273
36.	A. R Alimov, “Approximative solar properties of sets and local geometry of the unit sphere”, Lobachevskii Journal of Mathematics, 44:12 (2023), 5142–5148	6 ^[x]
37.	A. R. Alimov, “Universality theorems for asymmetric spaces”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 26:2 (2023), 2250017 , 11 pp.	5 ^[x]
38.	A. R. Alimov, I. G. Tsar'kov, “Classical problems of rational approximation”, Dokl. Math., 106:2 (2022), 305–307
39.	A. R. Alimov, “Continuity of the metric projection and local solar properties of sets”, Set-Valued Var. Anal., 27:1 (2019), 213–222	5 ^[x]
40.	Alexey R. Alimov, “Solarity of sets in max-approximation problems”, J. Fixed Point Theory Appl., 21:3 (2019), 76 , 11 pp.	5 ^[x]
41.	A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18	5 ^[x]
42.	A. R. Alimov, “Monotone path-connectedness of $R$-weakly convex sets in spaces with linear ball embedding”, Eurasian Math. J., 3:2 (2012), 21–30	5 ^[x]
43.	A. R. Alimov, “Chebyshev Compact Sets in the Plane”, Proc. Steklov Inst. Math., 219 (1997), 2–19
44.	A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317
45.	A. R. Alimov, “A monotone path-connected set with outer radially lower continuous metric projection is a strict sun”, Siberian Math. J., 58:1 (2017), 11–15
46.	A. R Alimov, H. Berens, “Examples of Chebyshev sets in matrix spaces”, J. Approx. Theory, 99:1 (1999), 44–53	4 ^[x]
47.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets that are unions of planes”, Russian Math. Surveys, 79:2 (2024), 361–362
48.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets composed of subspaces in asymmetric normed spaces”, Izv. Math., 88:6 (2024), 1032–1049
49.	A. R. Alimov, I. G. Tsar'kov, “Classical concepts of approximation theory in asymmetric CLUR-spaces”, Math. Notes, 116:3 (2024), 408–420
50.	A. R. Alimov, “Tomographic characterizations of suns in three-dimensional spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 2, 2022, 45–55
51.	A. R. Alimov, “Solarity of Chebyshev sets in dual spaces and uniquely remotal sets”, Lobachevskii J. Math., 42:4 (2021), 785–790	3 ^[x]
52.	A. R. Alimov, “Singularities of Solutions of the Eikonal Equation”, Differ. Equ., 55:10 (2019), 1311–1316
53.	A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
54.	A. R. Alimov, “Ogranichennaya strogaya solnechnost strogikh solnts v prostranstve $C(Q)$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2012, no. 6, 16–19 ; A. R. Alimov, “Bounded strict solar property of strict suns in the space $C(Q)$”, Moscow University Mathematics Bulletin, Moscow University Mechanics Bulletin, 68:1 (2013), 14–17	3 ^[x]
55.	A. R. Alimov, “On local properties of spaces implying monotone path-connectedness of suns”, J. Anal., 31 (2023), 2287–2295	2 ^[x]
56.	A. R. Alimov, “Mazur spaces and 4.3-intersection property of $(BM)$-spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:2 (2016), 133–137
57.	A. R. Alimov, “The Rainwater–Simons weak convergence theorem for the Brown associated norm”, Eurasian Math. J., 5:2 (2014), 126–131	2 ^[x]
58.	A. R. Alimov, “Geometric construction of Chebyshev sets in the spaces $\ell^\infty(n)$, $c_0$ and $c$”, Russian Math. Surveys, 60:3 (2005), 559–561
59.	A. R Alimov, “Hereditary properties of lower semicontinuous metric projection and solar properties of sets”, J. Anal., 33:2 (2025), 743–753	1 ^[x]
60.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and approximative properties of sets in asymmetric spaces”, Filomat, 38:9 (2024), 3243–3259	1 ^[x]
61.	A. R. Alimov, “Strict suns composed of planes”, Proc. Steklov Inst. Math. (Suppl.), 327, suppl. 1 (2024), S1–S9
62.	A. R. Alimov, “Geometricheskoe stroenie chebyshevskikh mnozhestv i solnts v trekhmernykh prostranstvakh s tsilindricheskoi normoi”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2020, no. 5, 26–32	1 ^[x]
63.	A. R. Alimov, “Bounded contractibility of strict suns in three-dimensional spaces”, J. Math. Sci., 250:3 (2020), 385–390
64.	A. R. Alimov, “Monotone path-connectedness of $R$-weakly convex sets in the space $C(Q)$”, J. Math. Sci., 185:3 (2012), 360–366
65.	A. R. Alimov, I. G. Tsar'kov, “Stability of best approximation in classical problems of geometric approximation theory”, Izv. RAN. Ser. Mat.
66.	A.R.Alimov,, N.A. Ilyasov, “Approximative compactness and acting points”, Russ. J. Math. Phys., 32:2 (2025), 219-227
67.	A. R. Alimov, I. G. Tsarkov, “Monotonno lineino svyaznye mnozhestva v geometricheskoi teorii priblizheniya i ee prilozheniyakh”, Matematika i teoreticheskie kompyuternye nauki, 2:2 (2024), 30-46
68.	A. R. Alimov, “Balayage theorems for connectedness problems in uniformly convex spaces”, Proc. Institute Math. Mech., 50:1 (2024), 53–61
69.	A. R. Alimov, I. G. Tsarkov, Sovremennaya geometricheskaya teoriya priblizhenii, “OntoPrint”, Moskva, 2023 , 425 pp.
70.	A. R. Alimov, I. G. Tsar'kov, “Max-solar properties of sets in normed and asymmetrically normed spaces”, J. Convex Analysis, 30:1 (2023), 159–174
71.	A. R. Alimov, I. G. Tsarkov, Spetskurs po klassicheskoi geometricheskoi teorii priblizhenii, OntoPrint, Moskva, 2021 , 210 pp.
72.	A. R. Alimov, E. V. Shchepin, “Suns are convex in tangent directions”, Dokl. Math., 99:1 (2019), 14–15
73.	Alexey R. Alimov, Evgeny V. Shchepin, “Convexity of Suns in Tangent Directions”, J. Convex Anal., 26:4 (2019), 1071–1076
74.	A. R. Alimov, I. G. Tsarkov, Geometricheskaya teoriya priblizhenii. Chast II. Priblizheniya klassami mnozhestv, dalneishee razvitie osnovnykh voprosov geometricheskoi teorii, OntoPrint, Moskva, 2018 , 350 pp.
75.	A. R. Alimov, “Vyborki iz operatorov nailuchshego i pochti nailuchshego priblizheniya i solnechnost mnozhestv”, Sovremennye problemy matematiki i ee prilozhenii, Materialy mezhdunarodnoi nauchnoi konferentsii (Dushanbe, 21–22.06.2018), Filial Moskovskogo gosudarstvennogo universiteta imeni M.V. Lomonosova v gorode Dushanbe, Tadzhikistan, 2018, 14–15
76.	A. R. Alimov, “On approximative properties of locally Chebyshev sets”, Proc. of Institute of mathematics and mechanics, 44:1 (2018), 36–42
77.	Alexey R. Alimov, Evgeny E. Bukzhalev, “Iteration method of approximate solution of the Cauchy problem for a singularly perturbed weakly nonlinear differential equation of an arbitrary order”, Turk. J. Math., 42:5 (2018), 2841–2853
78.	A. R. Alimov, “Lokalno chebyshevskie mnozhestva”, Vestnik Filiala Moskovskogo gosudarstvennogo universiteta imeni M.V. Lomonosova v gorode Dushanbe, 2:1 (2018), 5-11
79.	A. R. Alimov, I. G. Tsarkov, Geometricheskaya teoriya priblizhenii. Chast I. Klassicheskie ponyatiya i konstruktsii priblizheniya mnozhestvami, OntoPrint, Moskva, 2017 , 346 pp.
80.	A. R. Alimov, “O sootnoshenii mezhdu klassami solnts v nesimmetrichno normirovannykh prostranstvakh”, Trudy NIISI RAN, 7:1 (2017), 82–84
81.	A. R. Alimov, I. G. Tsarkov, Osnovy geometricheskoi teorii priblizhenii. Chast II. Vypuklost i svyaznost chebyshevskikh mnozhestv i solnts, Obschestvo s ogranichennoi otvetstvennostyu “OntoPrint”, Moskva, 2017 , 130 pp.
82.	A. R. Alimov, “$P$-svyaznoe lokalno chebyshëvskoe mnozhestvo yavlyaetsya chebyshëvskim”, Trudy Mezhdunarodnoi letnei matematicheskoi Shkoly-Konferentsii S.B. Stechkina po teorii funktsii (g. Dushanbe, 15–25 avgusta 2016 g.), Poligrafiya OOO "Ofset Dushanbe, Dushanbe, 2016, 32–35
83.	A. R. Alimov, “Svoistva peresecheniya sharov konechnomernykh (BM)-prostranstv”, Materialy mezhdunarodnoi konferentsii “Teoriya priblizhenii funktsii i rodstvennye zadachi analiza”, posvyaschennaya 100-letiyu so dnya rozhdeniya professora P. P. Korovkina, Teoriya priblizhenii funktsii i rodstvennye zadachi analiza (Kaluga, 09–10 oktyabrya 2015 g.), Izd-vo Kaluzhskogo gos. un-ta imeni K.E. Tsiolkovskogo, 2015, 17
84.	A. R. Alimov, “Solstice property for a system of 2-spaces”, East J. Approx., 4:1 (1998), 25–34
85.	A. R. Alimov, “Chebyshev set's complement”, East J. Approx., 2:2 (1996), 215–232
86.	A. R. Alimov, “A number of connected components of sun's complement”, East J. Approx., 1:4 (1995), 419–429
87.	A. R. Alimov, I. G. Tsar'kov, “Projection closed sets and Efimov–Stechkin spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 31, no. 3, 2025, 20–35
88.	A. R. Alimov, Mat. Pros., 2, MCCME, Moscow, 1998, 155–172
89.	A. R. Alimov, E. Berdysheva, P. Butzer, W.zu Castell, W. Dahmen, R. DeVore, F. Filibr, K. Jetter, H. Mhaskar, P. Nevai, T. Sauer, L. Schumaker, M. Sommer, H. Strauss, Hu Yu, “Hubert A. Berens (1936–2015)”, J. Approx. Theory, 198 (2015), iv–xxix	2 ^[x]
90.	A. R. Alimov, A. A. Vasil'eva, S. V. Konyagin, A. S. Kochurov, A. I. Kozko, T. P. Lukashenko, K. S. Ryutin, V. M. Tikhomirov, A. V. Fursikov, V. N. Chubarikov, “Igor Germanovich Tsarkov (to 60th anniversary)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 70–71
91.	A. R. Alimov, “Letter to the editor”, Math. Notes, 58:3 (1995), 1010

Presentations in Math-Net.Ru

1.	Weakly compact and Deutsch compact sets in approximation theory. Application to exponential sums A. R. Alimov Probability Techniques in Analysis and Algorithms on Networks November 25, 2025 15:50
2.	Слабо компактные и компактные по Дойчу множества в теории приближений. Приложения к экспоненциальным суммам I. G. Tsar'kov, A. R. Alimov Seminar on Theory of Functions of Real Variables November 14, 2025 18:30
3.	Приближение набором множеств. Кусочно аппроксимативно компактные чебышёвские множества. Солнечность ограниченно слабо компактных множеств I. G. Tsar'kov, A. R. Alimov Seminar on Theory of Functions of Real Variables November 7, 2025 18:30
4.	Аппроксимативная компактность для задач min- и max-аппроксимации A. R. Alimov Seminar on Theory of Functions of Real Variables November 22, 2024 18:30
5.	Связность множеств в несимметричных пространствах A. R. Alimov November 8, 2022 15:35
6.	Устойчивость, единственность и существование наилучшего приближения обобщенными дробно-рациональными функциями в $C(Q)$ и $L^p(Q)$ A. R. Alimov Differential equations, analysis and control: theory and applications October 24, 2022 18:25
7.	Солнечность и проксиминальность обобщенных дробно-рациональных функций в пространствах $C(Q)$ и $L^p$ A. R. Alimov Seminar on Theory of Functions of Real Variables March 18, 2022 18:30
8.	Some solar problems in $\max$- and $\min$-approximation A. R. Alimov International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin September 9, 2021 15:30
9.	Chebyshev sets and suns in a finite-dimensional space A. R. Alimov Optimization and nonlinear analysis February 4, 2021 14:00
10.	Выпуклость чебышёвских множеств и солнц по касательным направлениям A. R. Alimov Knots and Representation Theory March 11, 2019
11.	Решение задач о гладких C^1-решений уравнения эйконала, принцип отражения, зеркала I. G. Tsar'kov, A. R. Alimov Geometric Theory of Optimal Control March 14, 2018 18:30
12.	Локальные и глобальные аппроксимативно-геометрические свойства множеств A. R. Alimov Seminar on Approximation Theory November 16, 2017 10:30
13.	Selections from the best and near-best approximation operator A. R. Alimov International Conference "Mathematical Theory of Optimal Control" dedicated to the 90th birthday of Academician R. V. Gamkrelidze June 2, 2017 16:05
14.	Непрерывность метрической проекции, выборки из нее и солнечные свойства множеств A. R. Alimov March 21, 2017 17:30
15.	Солнечные свойства множеств непрерывной метрической проекции A. R. Alimov Seminar on Approximation Theory April 14, 2016 10:30
16.	Связность строгих солнц в конечномерных банаховых пространствах A. R. Alimov International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 25, 2015 14:30
17.	Свзяность солнц и чебышёвских множеств в задачах наилучшего приближения A. R. Alimov Seminar on Approximation Theory February 20, 2014 10:30

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