Persons: Tsar'kov, Igor' Germanovich

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Tsar'kov, Igor' Germanovich

Total publications:	100 (98)
in MathSciNet:	71 (70)
in zbMATH:	53 (52)
in Web of Science:	56 (55)
in Scopus:	62 (62)
Cited articles:	75
Citations:	689
Presentations:	11

Number of views:
This page:	5827
Abstract pages:	27535
Full texts:	7977
References:	3083

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

List of publications on ZentralBlatt

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

Full list of publications:

scientific publications

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


2024
1.	I. G. Tsar'kov, “$\theta$-metric function in the problem of minimization of functionals”, Izv. Math., 88:2 (2024), 369–388
2.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets that are unions of planes”, Russian Math. Surveys, 79:2 (2024), 361–362
3.	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. ;	3 ^[x]
4.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets composed of a union of subspaces in asymmetric normed spaces”, Izv. RAN. Ser. Mat. (to appear)

2024
5.	I. G. Tsar'kov, “Uniformly convex cone spaces and properties of convex sets in them”, Math. Notes, 116:4 (2024), 831–840
6.	A. R. Alimov, I. G. Tsar'kov, “Classical concepts of approximation theory in asymmetric CLUR-spaces”, Math. Notes, 116:3 (2024), 408–420
7.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and approximative properties of sets in asymmetric spaces”, Filomat, 38:9 (2024), 3243–3259 ;
8.	I. G. Tsar'kov, “Convexity of $\delta$-suns and $\gamma$-suns in asymmetric spaces”, Russ. J. Math. Phys., 31:2 (2024), 325-334
9.	I. G. Tsar'kov, “Properties of Sets in Asymmetric Spaces”, Lobachevskii Journal of Mathematics, 45:6 (2024), 2971–2974
10.	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

2023
11.	I. G. Tsar'kov, “Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces”, Izv. Math., 87:4 (2023), 835–851
12.	I. G. Tsar'kov, “Chebyshev Sets with Piecewise Continuous Metric Projection”, Math. Notes, 113:6 (2023), 840–849
13.	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
14.	I. G. Tsar'kov, “Kuhn–Tucker Type Theorems in Cone and Linear Normed Spaces”, Math. Notes, 114:6 (2023), 1373–1382
15.	I. G. Tsar'kov, “Connectedness in asymmetric spaces”, J. Math. Anal. Appl., 527:1 (2023), 127381 , 14 pp.
16.	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
17.	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 (2023), 128-134

2022
18.	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
19.	I. G. Tsar'kov, “Continuity of a Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 111:4 (2022), 616–623
20.	I. G. Tsar'kov, “Approximative and structural properties of sets in asymmetric spaces”, Izv. Math., 86:6 (2022), 1240–1253
21.	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. ;	15 ^[x]
22.	A. R. Alimov, I. G. Tsar'kov, “Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces”, Math. Notes, 112:1 (2022), 3–16
23.	I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Sb. Math., 213:10 (2022), 1444–1469
24.	A. R. Alimov, I. G. Tsarkov, “$\overset{\circ}B$-complete sets: approximative and structural properties”, Siberian Math. J., 63 (2022), 412–420
25.	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 ;	14 ^[x]
26.	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
27.	A. R. Alimov, I. G. Tsar'kov, “Classical problems of rational approximation”, Dokl. Math., 106:2 (2022), 305–307
28.	I. G. Tsar'kov, “Properties of Chebyshev generalized rational fractions in $L^1$”, Russian. J. Math. Phys., 29 (2022), 583-587
29.	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
30.	I. G. Tsar'kov, “Geometry of the singular set of hypersurfaces and the eikonal equation”, Russian. J. Math. Phys., 2022, 240-248
31.	I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Russian. J. Math. Phys., 29:1 (2022), 141-14

2016
32.	I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461

2021
33.	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. ;	7 ^[x]
34.	I. G. Tsar'kov, “Properties of Monotone Connected Sets”, Math. Notes, 109:5 (2021), 819–827
35.	I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Math. Notes, 110:5 (2021), 773–783
36.	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
37.	I. G. Tsar'kov, “Properties of Suns in the Spaces L1 and C(Q)”, Russian. J. Math. Phys., 28 (2021), 398-405

2020
38.	I. G. Tsar'kov, “The Geometry of a Singular Set of Hypersurfaces and the Eikonal Equation”, Math. Notes, 108:3 (2020), 426–433
39.	I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211

2019
40.	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
41.	I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008
42.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
43.	I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
44.	I. G. Tsar'kov, “Metric Max-Distance Function in Max-Approximation Problems”, Russ. J. Math. Phys., 26:2 (2019), 219-226

2018
45.	I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
46.	I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
47.	I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579
48.	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
49.	I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
50.	I. G. Tsar'kov, “Smoothing of Real-Valued Functions on Uniformly Smooth Spaces”, Russ. J. Math. Phys., 25 (2018), 409-414

2017
51.	I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669

2020
52.	I. G. Tsar'kov, “Some applications of geometric theory of approximations”, Journal of Mathematical Sciences, 245:1 (2020), 64–82

2017
53.	I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
54.	I. G. Tsar'kov, “Singular sets of surfaces”, Russ. J. Math. Phys., 24 (2017), 263–271
55.	I. G. Tsar'kov, “Properties of C^1-solution to the eikonal equation”, Lobachevskii J Math, 38:4 (2017), 762-765

2016
56.	I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461
57.	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
58.	I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285
59.	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

2011
60.	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]
61.	I. G. Tsar'kov, “Stability of Unique Solvability of Quasilinear Equations Given Additional Data”, Math. Notes, 90:6 (2011), 894–919
62.	I. G. Tsar'kov, “Properties of Sets Admitting Stable $\varepsilon$-Selections”, Math. Notes, 89:4 (2011), 572–576
63.	I. G. Tsar'kov, “Approximative compactness and nonuniqueness in variational problems, and applications to differential equations”, Sb. Math., 202:6 (2011), 909–934

2009
64.	I. G. Tsar'kov, “Stability of the unique solvability for some differential equations”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S185–S198

2006
65.	I. G. Tsar'kov, “Local Smoothing of Uniformly Smooth Maps”, Funct. Anal. Appl., 40:3 (2006), 200–206
66.	I. G. Tsar'kov, “Stability of Unique Solvability in an Ill-Posed Dirichlet Problem”, Math. Notes, 79:2 (2006), 268–282

2005
67.	I. G. Tsar'kov, “Smoothing of Hilbert-valued uniformly continuous maps”, Izv. Math., 69:4 (2005), 149–160
68.	I. G. Tsar'kov, “Localization of smooth and smoothing of uniformly continuous mappings”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S196–S210

2004
69.	I. G. Tsar'kov, “Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory”, Math. Notes, 75:2 (2004), 259–271

1999
70.	I. G. Tsar'kov, E. T. Shavgulidze, “Smooth Isometric Immersions into the Infinite-Dimensional Sphere”, Funct. Anal. Appl., 33:3 (1999), 239–240
71.	I. G. Tsar'kov, “Extension of Hilbert-valued Lipschitz mappings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, no. 6, 9–16

1997
72.	M. I. Karlov, I. G. Tsar'kov, “Convexity and connectedness of Chebyshev sets and suns”, Fundam. Prikl. Mat., 3:4 (1997), 967–978
73.	I. G. Tsar'kov, “Smoothing of functions in finite-dimensional Banach spaces”, Izv. Math., 61:1 (1997), 207–223
74.	I. G. Tsar'kov, “Smoothing of Functions on a Hilbert Ball”, Proc. Steklov Inst. Math., 219 (1997), 403–412

1996
75.	I. G. Tsar'kov, “On $\epsilon$-selections”, Dokl. Akad. Nauk, 349:6 (1996), 747–748
76.	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

1995
77.	I. G. Tsar'kov, “Polynomial Approximation of Vector Functions”, Funct. Anal. Appl., 29:3 (1995), 222–223
78.	I. G. Tsar'kov, “On the extension and smoothing of vector-valued functions”, Izv. Math., 59:4 (1995), 847–879
79.	I. G. Tsar'kov, “Some topics on the continuation and smoothing of vector functions”, Math. Notes, 58:6 (1995), 1327–1335
80.	I. G. Tsar'kov, “Right inverse operators and $\varepsilon$-selections”, Russian Math. Surveys, 50:2 (1995), 453–454
81.	I. G. Tsar'kov, “Some theorems on function smoothing”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 1, 79–81
82.	I. G. Tsar'kov, “Extension theorems and approximation of functions in Banach spaces”, Dokl. Math., 50:2 (1995), 348–350

1994
83.	I. G. Tsar'kov, “Linear methods in some smoothing problems”, Math. Notes, 56:6 (1994), 1255–1270

1995
84.	I. G. Tsar'kov, “Smoothing of abstract functions”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 405–430

1993
85.	I. G. Tsar'kov, “Smoothing of uniformly continuous mappings in $L_p$ spaces”, Math. Notes, 54:3 (1993), 957–967

1994
86.	I. G. Tsar'kov, “On global existence of an implicit function”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 287–313

1992
87.	I. G. Tsar'kov, “Theorems on the global existence of an implicit function and their applications”, Dokl. Math., 45:3 (1992), 638–640

1994
88.	I. G. Tsar'kov, “Widths and Jackson's type inequality for abstract functions”, Proc. Steklov Inst. Math., 198 (1994), 209–221

1990
89.	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
90.	I. G. Tsar'kov, “Continuity of the metric projection, structural and approximate properties of sets”, Math. Notes, 47:2 (1990), 218–227

1989
91.	I. G. Tsar'kov, “Local ‘homogeneity’ of sets of uniqueness”, Mat. Zametki, 45:5 (1989), 121–123

1990
92.	I. G. Tsar'kov, “The inequality of Jackson type for abstract functions”, Math. USSR-Sb., 67:1 (1990), 117–142
93.	I. G. Tsar'kov, “Compact and weakly compact Chebyshev sets in linear normed spaces”, Proc. Steklov Inst. Math., 189 (1990), 199–215

1988
94.	I. G. Tsar'kov, “Compact and weakly compact Chebyshev sets in linear normed spaces”, Dokl. Math., 37:3 (1988), 629–631
95.	S. V. Konyagin, I. G. Tsar'kov, “On smoothing of maps in normed spaces”, Russian Math. Surveys, 43:4 (1988), 213–214

1986
96.	I. G. Tsar'kov, “Relations between certain classes of sets in Banach spaces”, Math. Notes, 40:2 (1986), 597–610
97.	S. V. Konyagin, I. G. Tsar'kov, “Efimov–Stechkin spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, no. 5, 20–27

1984
98.	I. G. Tsar'kov, “Bounded Chebyshev sets in finite-dimensional Banach spaces”, Math. Notes, 36:1 (1984), 530–537

Presentations in Math-Net.Ru

1.	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
2.	Caustics, applications in natural sciences. Mach disks, reflection caustics. I. G. Tsar'kov Geometric Theory of Optimal Control October 6, 2021 16:45
3.	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
4.	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
5.	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
6.	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
7.	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
8.	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
9.	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
10.	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

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