01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
23.12.1954
E-mail:
Keywords:
Hardy spaces (complex and real, one-dimensional and multidimensional); shift operator; lacunary series; Schatten–von Neumann classes.
Main publications:
A. B. Aleksandrov, “Suschestvovanie vnutrennikh funktsii v share”, Matematicheskii sbornik, 118:2 (1982), 147–163
A. B. Aleksandrov, “Vnutrennie funktsii na kompaktnykh prostranstvakh”, Funktsionalnyi analiz i ego prilozheniya, 18:2 (1984), 1–13
A. B. Aleksandrov, “Teoriya funktsii v share”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 8, VINITI, M., 1985, 115–190
A. B. Aleksandrov, “Ortogonalnye bazisy iz vnutrennikh funktsii”, DAN SSSR, 306:2 (1989), 265–268
A. B. Aleksandrov, “Lakunarnye ryady i psevdoprodolzheniya. Arifmeticheskii podkhod”, Algebra i analiz, 9:1 (1997), 3–31
A. B. Aleksandrov, V. V. Peller, “Functions of perturbed noncommuting unbounded self-adjoint operators”, St. Petersburg Math. J., 34:6 (2023), 913–927
2022
10.
A. B. Aleksandrov, “On substitutions with a weight in the space of operator Lipschitz functions”, Investigations on linear operators and function theory. Part 50, Zap. Nauchn. Sem. POMI, 512, POMI, St. Petersburg, 2022, 5–14
11.
A. B. Aleksandrov, V. V. Peller, “Functions of pairs of unbounded noncommuting self-adjoint operators under perturbation”, Dokl. Math., 106:3 (2022), 407–411
2021
12.
A. B. Aleksandrov, “On the operator Lipschitz norm of the functions $z^n$ on a finite set of the unit circle”, Investigations on linear operators and function theory. Part 49, Zap. Nauchn. Sem. POMI, 503, POMI, St. Petersburg, 2021, 5–21
13.
A. B. Aleksandrov, E. Doubtsov, “Comparison of Clark Measures in Several Complex Variables”, Extended Abstracts Fall 2019, Trends in Mathematics, 12, Springer Nature, 2021, 9–16
A. B. Aleksandrov, V. V. Peller, D. S. Potapov, “On a Trace Formula for Functions of Noncommuting Operators”, Math. Notes, 106:4 (2019), 481–487
2020
21.
A. B. Aleksandrov, “Some remarks concerning operator Lipschitz functions”, J. Math. Sci. (N. Y.), 251:2 (2020), 176–189
2018
22.
A. B. Aleksandrov, “Interpolation by the derivatives of operator Lipschitz functions”, 50 Years with Hardy Spaces, Oper. Theory Adv. Appl., 261, Birkhäuser, Cham, 2018, 83–95
2017
23.
A. B. Aleksandrov, V. V. Peller, “Multiple operator integrals, Haagerup and Haagerup‐like tensor products, and operator ideals”, Bulletin London Math. Soc., 49:3 (2017), 463–479
A. B. Aleksandrov, F. L. Nazarov, V. V. Peller, “Functions of noncommuting self-adjoint operators under perturbation and estimates of triple operator integrals”, Advances in Math., 295:1 (2016), 1–52
A. B. Aleksandrov, V. V. Peller, “Operator Lipschitz functions”, Russian Math. Surveys, 71:4 (2016), 605–702
26.
A. Aleksandrov, V. Peller, “Functions of almost commuting operators and an extension of the Helton–Howe trace formula”, J. Funct. Anal., 271:11 (2016), 3300–3322
A. B. Aleksandrov, V. V. Peller, “Krein's trace formula for unitary operators and operator Lipschitz functions”, Funct. Anal. Appl., 50:3 (2016), 167–175
28.
A. B. Aleksandrov, “Commutator Lipschitz functions and analytic continuation”, J. Math. Sci. (N. Y.), 215:5 (2016), 543–551
2015
29.
A. Aleksandrov, F. Nazarov, V. Peller, “Functions of perturbed noncommuting self-adjoint operators”, C. R. Acad. Sci. Paris, Ser. I, 353:3 (2015), 209–214
A. Aleksandrov, V. Peller, “Almost commuting functions of almost commuting self-adjoint operators”, C. R. Acad. Sci. Paris, Ser. I, 353:7 (2015), 583–588
A. Aleksandrov, F. Nazarov, V. Peller, “Triple operator integrals in Schatten–von Neumann norms and functions of perturbed noncommuting operators”, C. R. Acad. Sci. Paris, Ser. I, 353:8 (2015), 723–728
A. B. Aleksandrov, V. V. Peller, “Functions of perturbed dissipative operators”, St. Petersburg Math. J., 23:2 (2012), 209–238
2011
37.
A. B. Aleksandrov, V. V. Peller, D. S. Potapov, F. A. Sukochev, “Functions of normal operators under perturbations”, Advances in Math., 226:6 (2011), 5216–5251
A. Aleksandrov, V. Peller, D. Potapov, F. Sukochev, “Functions of perturbed normal operators”, C. R. Acad. Sci. Paris, Ser. I, 348:9-10 (2010), 553–558
A. B. Aleksandrov, V. V. Peller, “Functions of perturbed unbounded self-adjoint operators. Operator Bernstein type inequalities”, Indiana Univ. Math. J., 59:4 (2010), 1451–1490
A. B. Aleksandrov, “Approximation in $L^p(\mathbb R^d)$, $0<p<1$, by linear combinations of characteristic functions of balls”, J. Math. Sci. (N. Y.), 165:4 (2010), 431–434
2009
45.
A. Alexandrov, G. Rozenblum, “Finite rank Toeplitz operators: Some extensions of D. Luecking’s theorem”, J. Funct. Anal., 256:7 (2009), 2291–2303
A. B. Aleksandrov, S. Janson, V. V. Peller, R. Rochberg, “An interesting class of operators with unusual Schatten-von Neumann behavior”, Proceedings of Conference on Function Spaces, Interpolation Theory, and related topics in honour of Jaak Peetre on his 65th birthday, Walter de Gruyter, Berlin, 2002, 61–149
55.
A. B. Aleksandrov, “A Class of Interpolating Blaschke Products and Best Approximation in $L^p$ for $p<1$”, Comput. Methods Funct. Theory, 2:2 (2002), 549–578
A. B. Aleksandrov, “Toeplitz–Schur multipliers of the class $S_p(L^2(G))$ for $p<1$”, J. Math. Sci. (N. Y.), 120:5 (2004), 1645–1652
2000
57.
A. B. Aleksandrov, “On embedding theorems for coinvariant subspaces of the shift operator. I”, Complex analysis, operators, and related topics, Oper. Theory Adv. Appl., v. 113, Birkhäuser, Basel, 2000, 45–64
A. B. Aleksandrov, “On the boundary decay in the mean of harmonic functions”, St. Petersburg Math. J., 7:4 (1996), 507–542
1997
66.
A. B. Aleksandrov, “On the existence of nontangential boundary values of pseudocontinuable functions”, J. Math. Sci. (New York), 87:5 (1997), 3781–3787
1995
67.
A. B. Aleksandrov, J. Bourgain, M. Giesecke, V. Havin, Yu. Vymenets, “Uniqueness and free interpolation for logarithmic potentials and the Cauchy problem for the Laplace equation in $\Bbb R^2$”, Geometric and Functional Analysis, 5:3 (1995), 529–571
A. B. Aleksandrov, “A simple proof of a theorem of Vol'berg and Treil' on the embeddings of coinvariant subspaces of the shift operator”, J. Math. Sci. (New York), 85:2 (1997), 1773–1778
69.
A. B. Aleksandrov, “On a maximum principle for pseudocontinuable functions”, J. Math. Sci. (New York), 85:2 (1997), 1767–1772
1994
70.
A. B. Aleksandrov, P. P. Kargaev, “The Hardy spaces $H^p(\Bbb R^d)$ and approximation in $L^p(\Bbb R^d)$ for $p < 1$”, Lect. Notes Math., 1573 (1994), 428–431
71.
A. B. Aleksandrov, P. P. Kargaev, “Hardy classes of functions that are harmonic in a half-space”, St. Petersburg Math. J., 5:2 (1994), 229–286
1990
72.
A. B. Aleksandrov, “On the Hardy class of functions harmonic in the half-space”, Séminaire d'Analyse Harmonique. Année 1989/90, Univ. Paris XI, Orsay, 1990, 9–10
1993
73.
A. B. Aleksandrov, “Inner functions and related spaces of pseudocontinuable functions”, J. Soviet Math., 63:2 (1993), 115–129
1989
74.
A. B. Aleksandrov, “Orthogonal bases of inner functions”, Soviet Math. Dokl., 39:3 (1989), 463–466
1987
75.
A. B. Aleksandrov, “Multiplicity of boundary values of inner functions”, Sov. J. Contemp. Math. Anal. Arm. Acad. Sci., 22:5 (1987), 74–87
76.
A. B. Aleksandrov, “Inner functions: results, methods, problems”, Proceedings of the International Congress of Mathematicians, Vol. 1 (Berkeley, 1986), Amer. Math. Soc., Providence, RI, 1987, 699–707
1986
77.
A. B. Aleksandrov, “Proper holomorphic mappings from the balll into a polydisk”, Sov. Math., Dokl., 33 (1986), 1–5
1988
78.
A. B. Aleksandrov, “Measurable partitions of the circumference, induced by inner functions”, J. Soviet Math., 42:2 (1988), 1610–1613
1994
79.
A. B. Aleksandrov, “Function theory in the ball”, Encyclopaedia Math. Sci., 8, Springer-Verlag, Berlin (1994), 107–178
1990
80.
A. B. Aleksandrov, “Blaschke's Condition and the Zeros of Bounded Holomorphic Functions”, Amer. Math. Soc. Transl., 146 (1990), 9–11
1984
81.
A. B. Aleksandrov, “Inner functions on compact spaces”, Funct. Anal. Appl., 18:2 (1984), 87–98
82.
A. B. Aleksandrov, V. P. Havin, “On the definition of $H^p(\Bbb R^n)$”, Lect. Notes Math., 1043 (1984), 346–346
83.
A. B. Aleksandrov, “Invariant subspaces of the backward shift operator in the Smirnov class”, Lect. Notes Math., 1043 (1984), 393–395
84.
A. B. Aleksandrov, “Inner functions on spaces of homogeneous type”, J. Sov. Math., 27 (1984), 2433–2437
1983
85.
A. B. Aleksandrov, “On boundary values of functions holomorphic in a ball”, Sov. Math., Dokl, 28 (1983), 134–137
86.
A. B. Aleksandrov, “Dva analoga teoremy M. Rissa o sopryazhënnykh funktsiyakh dlya prostranstv V.I. Smirnova $E^p$, $0<p<1$”, Teoriya operatorov i teoriya funktsii (Mezhvedomstv. sbornik), LGU, 1983, 9–20
87.
A. B. Aleksandrov, “The existence of inner functions in the ball”, Math. USSR-Sb., 46:2 (1983), 143–159
1982
88.
A. B. Aleksandrov, “The Hardy classes $H^p$ for $p<1$ and quasi-inner functions in the ball”, Sov. Math. Dokl., 25 (1982), 145–148
89.
A. B. Aleksandrov, “Svoistvo mazhoratsii dlya mnogomernykh klassov Khardi–Steina–Veisa”, Vestnik LGU, 13:3 (1982), 97–98
1981
90.
A. B. Aleksandrov, “$A$-integrability of the boundary values of harmonic functions”, Math. Notes, 30:1 (1981), 515–523
1983
91.
A. B. Aleksandrov, “Invariant subspaces of the shift operator. Axiomatic approach”, J. Soviet Math., 22:6 (1983), 1695–1708
1981
92.
A. B. Aleksandrov, “Essays on non locally convex Hardy classes”, Lect. Notes Math., 864 (1981), 1–89
A. B. Aleksandrov, “Invariant subspaces of the backward shift operator in the space $H^p$ ($p\in(0,1)$)”, Investigations on linear operators and function theory. Part IX, Zap. Nauchn. Sem. LOMI, 92, “Nauka”, Leningrad. Otdel., Leningrad, 1979, 7–29
94.
A. B. Aleksandrov, A. E. Dzhrbashyan, V. P. Khavin, “O formule Karlesona dlya integrala Dirikhle analiticheskoi funktsii”, Vestnik LGU, 19:4 (1979), 8–14
95.
A. B. Aleksandrov, “Approximation by rational functions, and an analogue of the M. Riesz theorem on conjugate functions for $L^p$-spaces with $p\in(0,1)$”, Math. USSR-Sb., 35:3 (1979), 301–316
1986
96.
A. B. Aleksandrov, “Discrete measures with compact nowhere dense support, orthogonal to rational functions”, J. Soviet Math., 34:6 (1986), 2023–2028
1975
97.
A. B. Aleksandrov, “Norm of the Hilbert transformation in a space of Hölder functions”, Funct. Anal. Appl., 9:2 (1975), 94–96