Azizov, Tomas Yakovlevich

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Total publications: 25
Scientific articles: 25

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Doctor of physico-mathematical sciences (1988)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 14.04.1946
Keywords: indefinite metric space; extensions of symmetric operators; basicity of root vectors.


The main object of researches is the operator theory in spaces with indefinite metrics. The invariant subspace theory for $J$-dissipative operators is developed, the basicity property for root vectors of $J$-dissipative operators is studied. There where introduced and researched special classes $(H, K(H))$ of $J$-dissipative operators and $J$-contractions, also some applications to the theory of small motions of a visco-elastic fluid are obtained. Problems in the extensions theory for isometric and symmetric operators in Krein spaces are investigated. It is obtained a representation of functions which are analytic in the origin via Krein space unitary operators.


Mathematics studies at the Zhitomir State Pedagogical Institute (1964–1965), and at the Voronezh State University (1966–1969), Post-gratuade study at the Voronezh State University by Prof. I. S. Iokhvidov (1969–1972), Candidate of Physics and Mathematics (1972), Thesis: "Dissipative Operators in a Hilbert Space with an Indefinite Metric", Doctor of Physics and Mathematics (1988), Thesis: "A Spectral and Extension Theory of Operators in Spaces with an Indefinite Inner Product".

Main publications:
  • Arocena R., Azizov T. Ya., Dijksma A., and Marcantognini S. A. M. On Commutant Lifting with Finite Defect. II // J. Funct. Anal., 1997, 144, no. 2, 105–116.
  • Azizov T. Ya., Dijksma A., Foerster K.-H., and Glaskova M. Yu. On the closedness of operator pencils // Indiana Univ. Math. J., 2000, 49, no. 1, 31–59.
  • Azizov T. Ya., Barsukov A. I., Dijksma A., and Jonas P. Similarity between Krein space bicontractions and Hilbert space contractions // Operator Theory: Advan. and Appl., v. 124, Birkhauser, 2001, 109–129.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. T. Ya. Azizov, M. V. Chugunova, “Pontryagin's Theorem and Spectral Stability Analysis of Solitons”, Mat. Zametki, 86:5 (2009),  643–658  mathnet  mathscinet  zmath  elib; Math. Notes, 86:5 (2009), 612–624  isi  scopus
2. T. Ya. Azizov, P. Jonas, “On Locally Definitizable Matrix Functions”, Funktsional. Anal. i Prilozhen., 41:3 (2007),  1–16  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 41:3 (2007), 169–180  isi  scopus
3. T. Ya. Azizov, L. I. Sukhocheva, V. A. Shtraus, “Operators in Krein Space”, Mat. Zametki, 76:3 (2004),  324–334  mathnet  mathscinet  zmath; Math. Notes, 76:3 (2004), 306–314  isi  scopus
4. T. Ya. Azizov, V. K. Kiriakidi, G. A. Kurina, “An Indefinite Approach to the Reduction of a Nonnegative Hamiltonian Operator Function to a Block Diagonal Form”, Funktsional. Anal. i Prilozhen., 35:3 (2001),  73–75  mathnet  mathscinet  zmath; Funct. Anal. Appl., 35:3 (2001), 220–221  isi  scopus
5. T. Ya. Azizov, V. A. Senderov, V. A. Khatskevich, “Geometry of $\mathfrak J$-Spaces and Properties of Reversing Operators”, Mat. Zametki, 69:3 (2001),  477–479  mathnet  mathscinet  zmath; Math. Notes, 69:3 (2001), 429–431  isi
6. T. Ya. Azizov, V. K. Kiriakidi, “Convexity and weak closedness of the image of operator balls under linear-fractional transformations”, Mat. Zametki, 67:2 (2000),  302–304  mathnet  mathscinet  zmath; Math. Notes, 67:2 (2000), 245–247  isi
7. T. Ya. Azizov, N. D. Kopachevskii, L. D. Orlova, “An operator approach to the study of the Oldroyd hydrodynamic model”, Mat. Zametki, 65:6 (1999),  924–928  mathnet  mathscinet  zmath; Math. Notes, 65:6 (1999), 773–776  isi
8. T. Ya. Azizov, A. I. Barsukov, “The algebraic structure of $H$-dissipative operators in a finite-dimensional space”, Mat. Zametki, 63:2 (1998),  163–169  mathnet  mathscinet  zmath; Math. Notes, 63:2 (1998), 145–149  isi
9. T. Ya. Azizov, V. L. Khatskevich, “On self-adjoint operators connected by inequalities and on their applications to problems of mathematical physics”, Mat. Zametki, 55:6 (1994),  3–12  mathnet  mathscinet  zmath; Math. Notes, 55:6 (1994), 549–554  isi
10. T. Ya. Azizov, V. L. Khatskevich, “Some applications of the theory of operators in Krein spaces to the solvability of nonlinear Hamiltonian systems”, Mat. Zametki, 50:4 (1991),  3–9  mathnet  mathscinet  zmath; Math. Notes, 50:4 (1991), 987–992  isi
11. T. Ya. Azizov, V. A. Khatskevich, D. M. Shoikhet, “On the number of fixed points of a holomorphism”, Sibirsk. Mat. Zh., 31:6 (1990),  192–195  mathnet  mathscinet  zmath; Siberian Math. J., 31:6 (1990), 1040–1042  isi
12. T. Ya. Azizov, S. S. Horuzhy, “Ghost number and ghost conjugation operators in the formalism of BRST quantization”, TMF, 80:1 (1989),  3–14  mathnet  mathscinet; Theoret. and Math. Phys., 80:1 (1989), 671–679  isi
13. T. Ya. Azizov, “Completeness of the system of root vectors of operators in a space with indefinite metric”, Funktsional. Anal. i Prilozhen., 21:1 (1987),  66–67  mathnet  mathscinet  zmath; Funct. Anal. Appl., 21:1 (1987), 56–58  isi
14. T. Ya. Azizov, “Extensions of $J$-isometric and $J$-symmetric operators”, Funktsional. Anal. i Prilozhen., 18:1 (1984),  57–58  mathnet  mathscinet  zmath; Funct. Anal. Appl., 18:1 (1984), 46–48  isi
15. T. Ya. Azizov, N. N. Kuznetsova, “On $p$-bases in a Pontryagin space”, Uspekhi Mat. Nauk, 38:1(229) (1983),  151  mathnet  mathscinet  zmath; Russian Math. Surveys, 38:1 (1983), 169  isi
16. T. Ya. Azizov, “On completeness and the basis property of the eigenvectors and associated vectors of $J$-selfadjoint operators of class $\mathscr{K}(\mathbf{H})$”, Dokl. Akad. Nauk SSSR, 253:5 (1980),  1033–1035  mathnet  mathscinet  zmath
17. T. Ya. Azizov, S. A. Khoroshavin, “Invariant subspaces of operators which act in a space with indefinite metric”, Funktsional. Anal. i Prilozhen., 14:4 (1980),  1–7  mathnet  mathscinet  zmath; Funct. Anal. Appl., 14:4 (1980), 247–252  isi
18. T. Ya. Azizov, I. S. Iokhvidov, “Linear operators in spaces with an indefinite metric and their applications”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 17 (1979),  113–205  mathnet  mathscinet  zmath; J. Soviet Math., 15:4 (1981), 438–490
19. T. Ya. Azizov, E. B. Usvyatsova, “The existence of special non-negative invariant subspaces of $J$-dissipative operators”, Sibirsk. Mat. Zh., 18:1 (1977),  216–218  mathnet  mathscinet  zmath; Siberian Math. J., 18:1 (1977), 158–159  isi
20. T. Ya. Azizov, “Dissipative operators in a Hilbert space with an indefinite metric”, Izv. Akad. Nauk SSSR Ser. Mat., 37:3 (1973),  639–662  mathnet  mathscinet  zmath; Math. USSR-Izv., 7:3 (1973), 639–660
21. T. Ya. Azizov, “On the invariant subspaces of a family of commuting operators in the space $\Pi_\varkappa$”, Funktsional. Anal. i Prilozhen., 6:3 (1972),  59–60  mathnet  mathscinet  zmath; Funct. Anal. Appl., 6:3 (1972), 220–221
22. T. Ya. Azizov, E. I. Iokhvidov, “Invariant subspaces of maximal $J$-dissipative operators”, Mat. Zametki, 12:6 (1972),  747–754  mathnet  mathscinet  zmath; Math. Notes, 12:6 (1972), 886–889
23. T. Ya. Azizov, “Invariant subspaces and completeness criteria for the root vector system of $J$-dissipative operators in the Pontrjagin space $\Pi_\kappa$”, Dokl. Akad. Nauk SSSR, 200:5 (1971),  1015–1017  mathnet  mathscinet  zmath
24. T. Ya. Azizov, “Spectra of certain classes of operators in Hilbert space”, Mat. Zametki, 9:3 (1971),  303–310  mathnet  mathscinet  zmath; Math. Notes, 9:3 (1971), 176–180
25. T. Ya. Azizov, I. S. Iokhvidov, “Linear operators in Hilbert spaces with $G$-metric”, Uspekhi Mat. Nauk, 26:4(160) (1971),  43–92  mathnet  mathscinet  zmath; Russian Math. Surveys, 26:4 (1971), 45–97

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