Persons: Tsar'kov, Igor' Germanovich

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Tsar'kov, Igor' Germanovich

Statistics
in MathSciNet:	80 (79)
in zbMATH:	70 (69)
in Web of Science:	58 (57)
in Scopus:	67 (67)

Professor

Doctor of physico-mathematical sciences (1996)

Speciality:

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

Birth date:

5.01.1960

E-mail:

Keywords:

approximations, smooth approximations, extension of maps.

Main publications:

Ogranichennye chebyshevskie mnozhestva v konechnomernykh banakhovykh prostranstvakh // Matematicheskie zametki. T. 36, # 1. 1984. S. 73–87.
O kompaktnykh i slabo kompaktnykh chebyshevskikh mnozhestvakh v lineinykh normirovannykh prostranstvakh // Trudy MIAN. T. 189. 1989. S. 169–184.
Neravenstvo tipa Dzheksona dlya abstraktnykh funktsii // Matematicheskii sbornik. T. 180, # 5. 1989. S. 121–123.
O globalnom suschestvovanii neyavnoi funktsii // Matematicheskii sbornik. T. 184, # 7. 1993. S. 79–116.
Sglazhivanie abstraktnykh funktsii // Matematicheskii sbornik. T. 185, # 11. 1994. S. 119–144.

https://www.mathnet.ru/eng/person8789

List of publications on Google Scholar

https://mathscinet.ams.org/mathscinet/MRAuthorID/212301

https://elibrary.ru/author_items.asp?authorid=7947

ISTINA

https://istina.msu.ru/workers/1227900

https://orcid.org/0000-0002-5943-3711

https://www.scopus.com/authid/detail.url?authorId=6602443197

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.	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
3.	I. G. Tsar'kov, “Relations between certain classes of sets in Banach spaces”, Math. Notes, 40:2 (1986), 597–610
4.	I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211
5.	I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
6.	I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Math. Notes, 110:5 (2021), 773–783
7.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
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.	I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461
10.	I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461
11.	I. G. Tsar'kov, “Properties of the sets that have a continuous selection from the operator $P^\delta$”, Math. Notes, 48:4 (1990), 1052–1058
12.	Alexey R. Alimov, Igor' G. Tsar'kov, “Ball-complete sets and solar properties of sets in asymmetric spaces”, Result. Math., 77 (2022), 86 , 1 pp.	22 ^[x]
13.	I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
14.	I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285
15.	I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579
16.	I. G. Tsar'kov, “Bounded Chebyshev sets in finite-dimensional Banach spaces”, Math. Notes, 36:1 (1984), 530–537
17.	I. G. Tsar'kov, “Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory”, Math. Notes, 75:2 (2004), 259–271
18.	A. R. Alimov, I. G. Tsarkov, “$\overset{\circ}B$-complete sets: approximative and structural properties”, Siberian Math. J., 63 (2022), 412–420
19.	I. G. Tsar'kov, “Properties of Sets Admitting Stable $\varepsilon$-Selections”, Math. Notes, 89:4 (2011), 572–576
20.	M. I. Karlov, I. G. Tsar'kov, “Convexity and connectedness of Chebyshev sets and suns”, Fundam. Prikl. Mat., 3:4 (1997), 967–978
21.	A. R. Alimov, I. G. Tsar'kov, “Solarity and proximinality in generalized rational approximation in spaces $C(Q)$ and $L^p$”, Russian. J. Math. Phys., 29 (2022), 291–305	15 ^[x]
22.	I. G. Tsar'kov, “On global existence of an implicit function”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 287–313
23.	I. G. Tsar'kov, “Continuity of the metric projection, structural and approximate properties of sets”, Math. Notes, 47:2 (1990), 218–227
24.	I. G. Tsar'kov, “Properties of Suns in the Spaces L1 and C(Q)”, Russian. J. Math. Phys., 28 (2021), 398-405	14 ^[x]
25.	I. G. Tsar'kov, “Smoothing of uniformly continuous mappings in $L_p$ spaces”, Math. Notes, 54:3 (1993), 957–967
26.	I. G. Tsar'kov, “Singular sets of surfaces”, Russ. J. Math. Phys., 24 (2017), 263–271	13 ^[x]
27.	I. G. Tsar'kov, “Geometry of the singular set of hypersurfaces and the eikonal equation”, Russian. J. Math. Phys., 2022, 240-248	11 ^[x]
28.	I. G. Tsar'kov, “Some applications of geometric theory of approximations”, Journal of Mathematical Sciences, 245:1 (2020), 64–82
29.	I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Russian. J. Math. Phys., 29:1 (2022), 141-14	10 ^[x]
30.	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]
31.	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]
32.	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
33.	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
34.	I. G. Tsar'kov, “Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function”, Izv. Math., 83:6 (2019), 1234–1258
35.	I. G. Tsar'kov, “Properties of C^1-solution to the eikonal equation”, Lobachevskii J Math, 38:4 (2017), 762-765	9 ^[x]
36.	S. V. Konyagin, I. G. Tsar'kov, “Efimov–Stechkin spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, no. 5, 20–27
37.	I. G. Tsar'kov, “Smoothness of solutions of the eikonal equation and regular points of their level surfaces”, Russ. J. Math. Phys., 30:2 (2023), 259 - 269	8 ^[x]
38.	I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
39.	I. G. Tsar'kov, “Compact and weakly compact Chebyshev sets in linear normed spaces”, Proc. Steklov Inst. Math., 189 (1990), 199–215
40.	I. G. Tsar'kov, “Estimates of the Chebyshev radius in terms of the MAX-metric function and the MAX-projection operator”, Russian J. Math. Phys., 30:1 (2023), 128-134	7 ^[x]
41.	I. G. Tsar'kov, “Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces”, Sb. Math., 213:2 (2022), 268–282
42.	A. R. Alimov, I. G. Tsar'kov, “Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces”, Math. Notes, 112:1 (2022), 3–16
43.	I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Sb. Math., 213:10 (2022), 1444–1469
44.	I. G. Tsar'kov, “The Geometry of a Singular Set of Hypersurfaces and the Eikonal Equation”, Math. Notes, 108:3 (2020), 426–433
45.	I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669
46.	I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
47.	I. G. Tsar'kov, “$\theta$-metric function in the problem of minimization of functionals”, Izv. Math., 88:2 (2024), 369–388
48.	I. G. Tsar'kov, “Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces”, Izv. Math., 87:4 (2023), 835–851
49.	I. G. Tsar'kov, “Chebyshev Sets with Piecewise Continuous Metric Projection”, Math. Notes, 113:6 (2023), 840–849
50.	I. G. Tsar'kov, “Convexity of $\delta$-suns and $\gamma$-suns in asymmetric spaces”, Russ. J. Math. Phys., 31:2 (2024), 325-334	5 ^[x]
51.	I. G. Tsar'kov, “Kuhn–Tucker Type Theorems in Cone and Linear Normed Spaces”, Math. Notes, 114:6 (2023), 1373–1382
52.	A. R. Alimov, I. G. Tsar'kov, “Classical problems of rational approximation”, Dokl. Math., 106:2 (2022), 305–307
53.	I. G. Tsar'kov, “Properties of Chebyshev generalized rational fractions in $L^1$”, Russian. J. Math. Phys., 29 (2022), 583-587	5 ^[x]
54.	I. G. Tsar'kov, “Approximative compactness and nonuniqueness in variational problems, and applications to differential equations”, Sb. Math., 202:6 (2011), 909–934
55.	I. G. Tsar'kov, “Linear methods in some smoothing problems”, Math. Notes, 56:6 (1994), 1255–1270
56.	S. V. Konyagin, I. G. Tsar'kov, “On smoothing of maps in normed spaces”, Russian Math. Surveys, 43:4 (1988), 213–214
57.	I. G. Tsar'kov, “Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 112:6 (2022), 1017–1024
58.	I. G. Tsar'kov, “Properties of Monotone Connected Sets”, Math. Notes, 109:5 (2021), 819–827
59.	I. G. Tsar'kov, “Stability of the relative Chebyshev projection in polyhedral spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 4, 2018, 235–245
60.	I. G. Tsar'kov, “Stability of Unique Solvability in an Ill-Posed Dirichlet Problem”, Math. Notes, 79:2 (2006), 268–282
61.	I. G. Tsar'kov, “On the extension and smoothing of vector-valued functions”, Izv. Math., 59:4 (1995), 847–879
62.	I. G. Tsar'kov, “Smoothing of abstract functions”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 405–430
63.	I. G. Tsar'kov, “Widths and Jackson's type inequality for abstract functions”, Proc. Steklov Inst. Math., 198 (1994), 209–221
64.	I. G. Tsar'kov, “Local ‘homogeneity’ of sets of uniqueness”, Mat. Zametki, 45:5 (1989), 121–123
65.	I. G. Tsar'kov, “Properties of at most countable unions of pairwise disjoint sets in asymmetric spaces”, Sb. Math., 216:2 (2025), 257–269
66.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets that are unions of planes”, Russian Math. Surveys, 79:2 (2024), 361–362
67.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets composed of subspaces in asymmetric normed spaces”, Izv. Math., 88:6 (2024), 1032–1049
68.	A. R. Alimov, I. G. Tsar'kov, “Classical concepts of approximation theory in asymmetric CLUR-spaces”, Math. Notes, 116:3 (2024), 408–420
69.	I. G. Tsar'kov, “Reflexivity for spaces with extended norm”, Russ. J. Math. Phys., 30:3 (2023), 399 - 417	3 ^[x]
70.	I. G. Tsar'kov, “Continuity of a Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 111:4 (2022), 616–623
71.	V. V. Arestov, V. I. Berdyshev, N. I. Chernykh, T. V. Demina, N. N. Kholschevnikova, S. V. Konyagin, Yu. N. Subbotin, S. A. Telyakovskii, I. G. Tsar'kov, V. A. Yudin, “Exposition of the lectures by S. B. Stechkin on approximation theory”, Eurasian Math. J., 2:4 (2011), 5–155	3 ^[x]
72.	I. G. Tsar'kov, “Stability of Unique Solvability of Quasilinear Equations Given Additional Data”, Math. Notes, 90:6 (2011), 894–919
73.	I. G. Tsar'kov, “Stability of the unique solvability for some differential equations”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S185–S198
74.	I. G. Tsar'kov, “Local Smoothing of Uniformly Smooth Maps”, Funct. Anal. Appl., 40:3 (2006), 200–206
75.	I. G. Tsar'kov, “On smooth selections from sets of almost Chebyshev centers”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 2, 92–94
76.	I. G. Tsar'kov, “Compact and weakly compact Chebyshev sets in linear normed spaces”, Dokl. Math., 37:3 (1988), 629–631
77.	I. G. Tsar'kov, “Metric Max-Distance Function in Max-Approximation Problems”, Russ. J. Math. Phys., 26:2 (2019), 219-226	2 ^[x]
78.	I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
79.	I. G. Tsar'kov, E. T. Shavgulidze, “Smooth Isometric Immersions into the Infinite-Dimensional Sphere”, Funct. Anal. Appl., 33:3 (1999), 239–240
80.	I. G. Tsar'kov, “Extension of Hilbert-valued Lipschitz mappings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, no. 6, 9–16
81.	I. G. Tsar'kov, “Smoothing of functions in finite-dimensional Banach spaces”, Izv. Math., 61:1 (1997), 207–223
82.	I. G. Tsar'kov, “Smoothing of Functions on a Hilbert Ball”, Proc. Steklov Inst. Math., 219 (1997), 403–412
83.	I. G. Tsar'kov, “On $\epsilon$-selections”, Dokl. Akad. Nauk, 349:6 (1996), 747–748
84.	I. G. Tsar'kov, “Polynomial Approximation of Vector Functions”, Funct. Anal. Appl., 29:3 (1995), 222–223
85.	I. G. Tsar'kov, “Some topics on the continuation and smoothing of vector functions”, Math. Notes, 58:6 (1995), 1327–1335
86.	I. G. Tsar'kov, “Right inverse operators and $\varepsilon$-selections”, Russian Math. Surveys, 50:2 (1995), 453–454
87.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and approximative properties of sets in asymmetric spaces”, Filomat, 38:9 (2024), 3243–3259	1 ^[x]
88.	I.G Tsar'kov., “Relations between various types of suns in asymmetric spaces”, Russ. J. Math. Phys., 31 (2024), 562-567	1 ^[x]
89.	I. G. Tsar'kov, “Local and global suns”, Russ. J. Math. Phys., 31:4 (2024), 765–773	1 ^[x]
90.	I. G. Tsar'kov, “Approximative and structural properties of sets in asymmetric spaces”, Izv. Math., 86:6 (2022), 1240–1253
91.	I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008
92.	I. G. Tsar'kov, “Theorems on the global existence of an implicit function and their applications”, Dokl. Math., 45:3 (1992), 638–640
93.	I. G. Tsar'kov, “The inequality of Jackson type for abstract functions”, Math. USSR-Sb., 67:1 (1990), 117–142
94.	I.G.Tsar'kov, “Convexity of weakly compact sets in normed linear spaces”, Russ. J. Math. Phys., 32:3 (2025), 585–589
95.	I.G.Tsar'kov, “Solarity of boundedly ae-compact sets”, Russ. J. Math. Phys., 32:2 (2025), 410-415
96.	I. G. Tsar'kov, “Uniformly convex cone spaces and properties of convex sets in them”, Math. Notes, 116:4 (2024), 831–840
97.	I. G. Tsar'kov, “Properties of Sets in Asymmetric Spaces”, Lobachevskii Journal of Mathematics, 45:6 (2024), 2971–2974
98.	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
99.	I. G. Tsar'kov, “Connectedness in asymmetric spaces”, J. Math. Anal. Appl., 527:1 (2023), 127381 , 14 pp.
100.	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
101.	I. G. Tsar'kov, “Smoothing of Real-Valued Functions on Uniformly Smooth Spaces”, Russ. J. Math. Phys., 25 (2018), 409-414
102.	I. G. Tsar'kov, “Smoothing of Hilbert-valued uniformly continuous maps”, Izv. Math., 69:4 (2005), 149–160
103.	I. G. Tsar'kov, “Localization of smooth and smoothing of uniformly continuous mappings”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S196–S210
104.	I. G. Tsar'kov, “Some theorems on function smoothing”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 1, 79–81
105.	I. G. Tsar'kov, “Extension theorems and approximation of functions in Banach spaces”, Dokl. Math., 50:2 (1995), 348–350
106.	I. G. Tsar'kov, “Solarity of boundedly weakly compact sets”, Math. Notes, 117:4 (2025), 650–655
107.	A. R. Alimov, I. G. Tsar'kov, “Stability of best approximation in classical problems of geometric approximation theory”, Izv. RAN. Ser. Mat.
108.	I. G. Tsar'kov, “Density of points of continuity of the distance function for union of half-spaces in asymmetric spaces”, Math. Notes, 118:3 (2025), 614–623
109.	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
110.	N. N. Andreev, S. V. Konyagin, A. G. Sergeev, Yu. N. Subbotin, S. A. Telyakovskii, N. N. Kholshchevnikova, I. G. Tsar'kov, “International conference “Approximation theory” (Moscow, 23–26 august 2010)”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 314–315
111.	V. I. Berdyshev, V. A. Kaminsky, S. V. Konyagin, B. P. Osilenker, M. V. Samokhin, S. A. Telyakovskii, I. G. Tsar'kov, V. A. Shmatkov, “Alexandr L'vovich Garkavi (obituary)”, Russian Math. Surveys, 63:3 (2008), 547–549

Presentations in Math-Net.Ru

1.	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
2.	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
3.	Mach disks and caustic reflections, caustics, application to astrophysics I. G. Tsar'kov Weekly Mathematics Research Seminars at ADA University March 1, 2022 16:00
4.	Caustics, applications in natural sciences. Mach disks, reflection caustics. I. G. Tsar'kov Geometric Theory of Optimal Control October 6, 2021 16:45
5.	Caustics, Mach disks, application to astrophysics I. G. Tsar'kov International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin September 9, 2021 12:30
6.	Mach disks and caustic reflections, caustics, application to astrophysics I. G. Tsar’kov Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis – 2021 July 6, 2021 16:10
7.	Законы преломления и отражения в неевклидовых пространствах, каустика, приложения к астрофизике I. G. Tsar'kov Differential equations, analysis and control: theory and applications March 15, 2021 18:25
8.	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
9.	Экстремумы функции-расстояния, уравнение эйконала и связанные с ним геометрические задачи I. G. Tsar'kov Differential equations, analysis and control: theory and applications February 12, 2018 18:25
10.	Гладкие решения уравнения эйконала и поведение локальных минимумов функции расстояния I. G. Tsar'kov Seminar on Theory of Functions of Real Variables December 1, 2017 18:30
11.	Слабо монотонные множества относительно определяющих множеств. Связь с непрерывными $(r,\varepsilon)$-выборками I. G. Tsar'kov Seminar on Approximation Theory November 2, 2017 10:30
12.	Достаточные условия существования непрерывной $\varepsilon$-выборки I. G. Tsar'kov International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 25, 2015 17:55

Organisations