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Khazanov, Vladimir Borisovich
Statistics Math-Net.Ru
Total publications: 35
Scientific articles: 33

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Khazanov, Vladimir Borisovich
Professor
Doctor of physico-mathematical sciences (2006)
Speciality: 01.01.07 (Computing mathematics)
Birth date: 22.06.1947
E-mail: , ,
Website: https://www.smtu.ru/ru/viewperson/142/
Keywords: multiparameter polynomial and rational matrices and vectors, spectrum regular and singular, polynomial basis of null-space, pole-zero structure, rank factorization, rezultant matrix, inverse eigenvalue problems.
UDC: 512.83, 512.86, 517.41, 517.55, 518.12, 518.5, 519.614.2, 519.614.4, 519.615.2, 519.615.4, 519.615.5, 681.3, 519, 519.61, 519.6, 518.512, 518, 5I8.5I2.86
MSC: 15A18, 15A21, 15A22, 15A23, 15A24, 15A29, 15A54, 15A69, 47A10, 47A56,
47A80, 65D15, 65F15, 65F18, 65H10, 65H17

Subject:

The multiparameter (including one-parameter) polynomial and rational matrices (as regular, as singular) and vector spaces are the investigation object. The definitions of the base spectral characteristics (a polynomial basis of a null-space of a matrix; the finite and "infinite" spectrum, the regular and singular parts of the spectrum, an eigenvector and a Jordan semilattice of the vectors of a polynomial matrix; a pole-zero structure of a rational matrix) for the multiparameter matrices, consistent with the classical definitions for one-parameter case, were introduced. The generalized definitions: an eigenpolynomial, the generating eigenvector and principal vector, a free basis were introduced. The properties of these characteristics were investigated. The linearization of a polynomial matrix, realized by passage to an accompanying pencil of the constant matrices, is proposed. The representations of a rational matrix in the form MFD and PFD are considered, their properties are investigated. The rank factorization methods for the polynomial and rational matrices, which allow solving some partial multiparameter spectral problems, are developed. The methods for solving the multiparameter problems of algebra based on the resultant approach are developed. The methods of solving "connected" multiparameter spectral problems, are developed. The applications of the mentioned problems are particularly the problem of solving systems of nonlinear algebraic and rational equations and the inverse eigenvalue problems for a matrix (including additive and multiplicative problems).

Biography

Graduated from Leningrad Shipbuilding Institute specialized in "Computers" in 1971 (department of applied and computing mathematics, diploma supervisor — Kublanovskaya V. N.). Ph.D. thesis was defended in Leningrad State University in 1983 (science supervisor — Kublanovskaya V. N.). D.Sci. thesis "Multiparameter spectral problems for polynomial and rational matrices. Methods for solving multiparameter problems of algebra" was defended in St. Peetrsburg State University in 2006. A list of my works contains 70 titles.
   
Main publications:
  1. V. B. Khazanov, “METHODS FOR SOLVING SOME PARAMETRIC PROBLEMS OF ALGEBRA”, JOURNAL OF MATHEMATICAL SCIENCES, 137:3 (2006), 4852-4861
  2. V.B. Khazanov, “THE RESULTANT APPROACH TO COMPUTING VECTOR CHARACTERISTICS OF MULTIPARAMETER POLYNOMIAL MATRICES”, JOURNAL OF MATHEMATICAL SCIENCES, 137:3 (2006), 4862-4878
  3. V. B. Khazanov, “ON SOME SPECTRAL CHARACTERISTICS OF MULTIPARAMETER POLYNOMIAL MATRICES”, JOURNAL OF MATHEMATICAL SCIENCES, 132:2 (2006), 236-239
  4. V.B. Khazanov, “ON SOME PROPERTIES OF POLYNOMIAL BASES OF SUBSPACES OVER THE FIELD OF RATIONAL FUNCTIONS IN SEVERAL VARIABLES”, JOURNAL OF MATHEMATICAL SCIENCES, 121:4 (2004), 2538-2545
  5. V.B. Khazanov, “BALANCE RELATION FOR THE SPECTRAL CHARACTERISTICS OF A MULTIPARAMETER POLYNOMIAL MATRIX”, JOURNAL OF MATHEMATICAL SCIENCES, 165:5 (2010), 597-600

https://www.mathnet.ru/eng/person17701
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/212171
https://elibrary.ru/author_items.asp?authorid=6137

Publications in Math-Net.Ru Citations
2021
1. V. B. Khazanov, “Computation of Jordan vector semilattices of a multiparameter polynomial matrix”, Zap. Nauchn. Sem. POMI, 504 (2021),  172–180  mathnet
2020
2. V. B. Khazanov, “Computation of Jordan semi-lattices of vectors of a multiparameter polynomial matrix”, Zap. Nauchn. Sem. POMI, 496 (2020),  182–194  mathnet 1
2019
3. V. B. Khazanov, “Computation of a minimal basis of the right null space of a singular multiparameter polynomial matrix”, Zap. Nauchn. Sem. POMI, 482 (2019),  272–287  mathnet 3
4. V. B. Khazanov, “Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix”, Zap. Nauchn. Sem. POMI, 482 (2019),  259–271  mathnet 2
2011
5. V. N. Kublanovskaya, V. B. Khazanov, “To solving spectral problems for $q$-parameter polynomial matrices. 2”, Zap. Nauchn. Sem. POMI, 395 (2011),  162–171  mathnet  mathscinet; J. Math. Sci. (N. Y.), 182:6 (2012), 834–838  scopus 3
2010
6. V. N. Kublanovskaya, V. B. Khazanov, “To solving problems of algebra for two-parameter matrices. 7”, Zap. Nauchn. Sem. POMI, 382 (2010),  141–149  mathnet; J. Math. Sci. (N. Y.), 176:1 (2011), 78–82  scopus 3
2009
7. V. B. Khazanov, “Balance relation for the spectral characteristics of a multiparameter polynomial matrix”, Zap. Nauchn. Sem. POMI, 367 (2009),  187–194  mathnet; J. Math. Sci. (N. Y.), 165:5 (2010), 597–600  scopus 2
8. V. N. Kublanovskaya, V. B. Khazanov, “To solving problems of algebra for two-parameter matrices. 6”, Zap. Nauchn. Sem. POMI, 367 (2009),  171–186  mathnet; J. Math. Sci. (N. Y.), 165:5 (2010), 589–596  scopus 1
2008
9. V. N. Kublanovskaya, V. B. Khazanov, “To solving problems of algebra for two-parameter matrices. 3”, Zap. Nauchn. Sem. POMI, 359 (2008),  166–207  mathnet  zmath; J. Math. Sci. (N. Y.), 157:5 (2009), 761–783  scopus 4
2006
10. V. B. Khazanov, “Corrigendum to “Methods for solving some parameter problems of algebra””, Zap. Nauchn. Sem. POMI, 334 (2006),  232  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 141:6 (2007), 1701  scopus 2
11. V. B. Khazanov, “To solving spectral problems for multiparameter polynomial matrices”, Zap. Nauchn. Sem. POMI, 334 (2006),  212–231  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 141:6 (2007), 1690–1700  scopus 9
12. V. N. Kublanovskaya, V. B. Khazanov, “To solving inverse eigenvalue problems for parametric matrices”, Zap. Nauchn. Sem. POMI, 334 (2006),  174–192  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 141:6 (2007), 1668–1677  scopus 3
2005
13. V. B. Khazanov, “A resultant approach to computing vector characteristics of multiparameter polynomial matrices”, Zap. Nauchn. Sem. POMI, 323 (2005),  182–214  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 137:3 (2006), 4862–4878  scopus 6
14. V. B. Khazanov, “Methods for solving some parameter problems of algebra”, Zap. Nauchn. Sem. POMI, 323 (2005),  164–181  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 137:3 (2006), 4852–4861  scopus 6
2004
15. V. B. Khazanov, “On some spectral characteristics of multiparameter polynomial matrices”, Zap. Nauchn. Sem. POMI, 309 (2004),  166–173  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 132:2 (2006), 236–239
16. V. N. Kublanovskaya, V. B. Khazanov, “Modifications of the $\Delta W$-$q$ factorization method for multiparameter polynomial matrices and their properties”, Zap. Nauchn. Sem. POMI, 309 (2004),  154–165  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 132:2 (2006), 229–235 3
2003
17. V. B. Khazanov, “Methods for solving spectral problems for multiparameter matrix pencils”, Zap. Nauchn. Sem. POMI, 296 (2003),  139–168  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 127:3 (2005), 2033–2050 4
2002
18. V. B. Khazanov, “On some properties of polynomial bases of subspaces over the field of rational functions in several variables”, Zap. Nauchn. Sem. POMI, 284 (2002),  177–191  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 121:4 (2004), 2538–2545 9
19. V. N. Kublanovskaya, V. B. Khazanov, “To the solution of partial eigenproblems for polynomial matrices”, Zap. Nauchn. Sem. POMI, 284 (2002),  163–176  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 121:4 (2004), 2530–2537 1
2000
20. V. B. Khazanov, “On some properties of the minimal in degree irreducible factorizations of a rational matrix”, Zap. Nauchn. Sem. POMI, 268 (2000),  185–189  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 114:6 (2003), 1860–1861 1
1998
21. V. B. Khazanov, “Generating eigenvectors of a multiparameter polynomial matrix”, Zap. Nauchn. Sem. POMI, 248 (1998),  165–186  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 101:4 (2000), 3326–3337 6
22. V. N. Kublanovskaya, V. B. Khazanov, “Irreducible factorizations of $q$-parameter rational matrices”, Zap. Nauchn. Sem. POMI, 248 (1998),  147–164  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 101:4 (2000), 3315–3325 2
1996
23. V. N. Kublanovskaya, V. B. Khazanov, “Relative factorization of polynomials of several variables”, Zh. Vychisl. Mat. Mat. Fiz., 36:8 (1996),  6–11  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 36:8 (1996), 983–987  isi 4
1995
24. V. B. Khazanov, “On spectral properties of multiparameter polynomial matrices”, Zap. Nauchn. Sem. POMI, 229 (1995),  284–321  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 89:6 (1998), 1775–1800 14
1994
25. V. B. Khazanov, “Multiparameter eigenvalue probolems: Jordan semilattices of vectors”, Zap. Nauchn. Sem. POMI, 219 (1994),  213–220  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 86:4 (1997), 2944–2949 3
26. V. N. Kublanovskaya, V. B. Khazanov, “On irreducible factorization of rational matrices and their applications”, Zap. Nauchn. Sem. POMI, 219 (1994),  117–157  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 86:4 (1997), 2880–2906 3
1992
27. V. N. Kublanovskaya, V. B. Khazanov, “Spectral problems for pencils of polynomial matrices. Methods and algorithms. V”, Zap. Nauchn. Sem. POMI, 202 (1992),  26–70  mathnet  mathscinet  zmath; J. Math. Sci., 79:3 (1996), 1048–1076 3
1984
28. V. B. Khazanov, “Some spectral characteristics of $\lambda$-matrices”, Zap. Nauchn. Sem. LOMI, 139 (1984),  111–124  mathnet  mathscinet  zmath; J. Soviet Math., 36:2 (1987), 251–261 2
1981
29. V. B. Khazanov, “Spectral properties of $\lambda$-matrices”, Zap. Nauchn. Sem. LOMI, 111 (1981),  180–194  mathnet  mathscinet  zmath; J. Soviet Math., 24:1 (1984), 121–132 1
1976
30. V. N. Kublanovskaya, T. N. Smirnova, V. B. Khazanov, “Solving the eigenvalue problem for sparse matrices”, Zap. Nauchn. Sem. LOMI, 58 (1976),  92–110  mathnet  zmath; J. Soviet Math., 13:2 (1980), 261–275 3
31. V. N. Kublanovskaya, V. B. Mikhailov, V. B. Khazanov, “Eigenvalue problem for an irregular $\lambda$-matrix”, Zap. Nauchn. Sem. LOMI, 58 (1976),  80–92  mathnet  mathscinet  zmath; J. Soviet Math., 13:2 (1980), 251–260 1
1973
32. V. B. Khazanov, “A note for Danilewski' s method”, Zap. Nauchn. Sem. LOMI, 35 (1973),  142–145  mathnet  mathscinet  zmath
1971
33. V. N. Kublanovskaya, V. B. Khazanov, “On one inverse eigenvalue problem of matrix”, Zap. Nauchn. Sem. LOMI, 23 (1971),  84–93  mathnet  mathscinet  zmath
2013
34. M. K. Kerimov, L. Yu. Kolotilina, T. Ya. Kon'kova, V. N. Simonova, V. B. Khazanov, “In memory of Professor Vera Nikolaevna Kublanovskaya”, Zh. Vychisl. Mat. Mat. Fiz., 53:1 (2013),  163–168  mathnet  elib
2000
35. T. Ya. Kon'kova, V. N. Simonova, V. B. Khazanov, “Vera Nikolaevna Kublanovskaya. Short biography”, Zap. Nauchn. Sem. POMI, 268 (2000),  5–8  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 114:6 (2003), 1755–1756 1

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